PHYSICS
Answers Worksheet - 1
Chapter - 1 (Motion)
(a) 2as = v2 – u2
(a) 0.2 ms–2 and – 0.5 ms–2
(a) Speed
(c) Random Motion
An object can have zero displacement even when it has moved a distance. This takes place
when the final position of an object coincides with its own initial position. For example, if
a person moves around a circular area and comes back to the place from where he started
then the displacement will be zero.
Ans. 6. Here, the speed of sound v = 340 m/s ; d = 560 m.
Since the total distance covered by sound is two times the distance between the gunman
and the cliff is d.
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
We have,
v×t
2
560 × 2
t =
= 3.29 sec
340
d =
Ans. 7. Given :
h = 30 m
Initial velocity when the object is dropped from a height is zero.
i.e., u = 0 ms–1.
Time taken to reach the ground is given by
1
h = ut + gt 2
2
..
1
h = gt 2
( . u = 0 m/s)
2
30 × 2
t2 =
=6
10
t = 2·44 s
Final velocity is given by,
v = u + gt
v = 0 + 10 × 2.44 = 24.4 ms–1
Ans. 8. No. If the displacement is zero then it is not necessary that the distance travelled will also
be zero. If we are moving on a circular track whose initial and final positions are the same
and which is of 10 m circumference then the displacement would be zero but the distance
travelled would be 10 m.
Ans. 9. Distance travelled by the pulse, s = 10 m
Time taken, t = 0.6 s
Frequency, ν = 150 Hz
(a) We know that
distance s 10
v =
= 16.66 ms–1
= =
time
t 0.6
Hence, the velocity of the pulse is 16.66 m/s
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(b) We know that
v = nl
v 16.66
l = =
= 0.11 m
ν 150
Hence, the wavelength of the pulse is 0.11 m
Ans. 10. Velocity is defined as the rate of change of displacement will respect to time.
The S.I. unit of velocity is m/s.
Velocity depends upon magnitude as well as the direction, therefore, it is a vector quantity.
Ans. 11. (a) The velocity of a body can be changed in the following ways :
(i) By changing the speed of the body.
(ii) By keeping the speed constant but by changing the direction of the body.
(b) A body has a uniform velocity if it travels in a specific direction in a straight line and
moves over equal distances in equal intervals of time.
Ans. 12. When bodies of different masses are dropped at the same time from the same height, they
will reach the ground at the same time. It is because the acceleration due to gravity does
not depend on the mass of an object. It only depends on the gravitational constant, mass of
the Earth and square of the radius of the Earth.
Ans. 13. (a) The rate of change of velocity with respect to time is called acceleration.
v−u
Formula :
a =
t
Example : Any physical object will start accelerating if it is applied upon by an external
force. Example : a cricket ball is hitting with a bat.
(b) Initial velocity, u = 0 m/s
Final velocity, v = 10 m/s
Time, t = 15 minutes = 15 × 60 sec = 900 sec
v = u + at
v − u 10 − 0
=
a =
= 0.011 ms–1
900
t
Acceleration of the car = 0.011 m/s2.
(c) Distance travelled by the car during this time.
1
s = ut + at 2
2
1
s = 0 + × 0.011 × (900)2
2
s = 4455 m
s = 4.45 km
Ans. 14. (a) Retardation is also called as deceleration or negative acceleration. It is called negative
acceleration when velocity goes on decreasing. Retardation is a vector quantity.
(b) Initial velocity, u = 40 m/s
Final velocity, v = 30 m/s
v = u + at
30 = 40 + a × 5
a =–2
\ Acceleration of the bike is – 2 ms–1
(c) Distance travelled by bike during this time :
1
s = ut + at 2
2
1
2
s = 40 × 5 + × − 2 × (5)
2
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s = 200 – 25 = 175 m
Ans. 15. (a)
Total distance travelled = 250 km + 250 km = 500 km
Total time taken = 4 + 4 = 8 hr
Total distance travelled 500
= 62.5 km h–1
=
Average speed =
Total time taken
8
Thus, the average speed is 62.5 km h–1
(b)
Total displacement = 250 km – 250 km = 0 km
Total time taken = 8 hr
Average velocity =
Ans. 16. (a) We are given that
and
(i) We know,
Total displacement 0
–1
= = 0 km h
Total time taken
8
u = 18 km h–1 = 5 ms–1
v = 36 km h–1 = 10 ms–1
t =5s
v−u
a =
t
10 − 5
= 1 m s–2
5
a =
s = ut +
(ii) We know,
1 2
at
2
s = 5 × 5 + 1 × 1 × ( 5 )2
2
s = 25 + 12.5 m
= 37.5 m
The acceleration of the car is 1 m/s2 and the distance covered is 37.5 m.
(b) We are given that
a = – 6 ms–2, t = 2 s and v = 0 ms–1
v = u + at
0 =u–6×2
u = 12 ms–2
Now, we know
1
s = ut + at 2
2
s = 12 × 2 +
s = 24 – 12
s = 12 m
1
× ( − 6 ) ( 2 )2
2
Thus, the car will move 12 m before it stops after the application of brakes.
Ans. 17. (d) Displacement is the minimum distance between the starting and end point. The
displacement can be zero, if the object that started from its initial point comes back to the
same point. Therefore assertion is false and reason is true.
Ans. 18. (d)Here assertion is false and reason is true. Speed has only magnitude while velocity
has both magnitude and direction. So speed is a scalar quantity but velocity is a vector
quantity.
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Ans. 19. The rate of motion of an object can be → more comprehensive if we specify its direction
of motion along with its speed. The quantity that specifies both these aspects is called →
velocity. Velocity is the speed of an object moving in a definite direction. The velocity of an
object can be → uniform or variable. It can be changed by changing the → speed of object.
direction of motion or both. When an object is moving along a → straight line at a variable
speed, we can express the → magnitude of its rate of motion in terms of average velocity.
It is calculated in the same way as we calculate → the average speed.
(Words marked in BOLD are new information which is not mentioned.)
Ans. 20. If you carefully note, on being released, the stone moves along a straight line tangential
to the circular path. This is because once the stone is released, it continues to move along
the direction it has been moving at that instant. This shows that the direction of motion
changed at every point when the stone was moving along the circular path.
Ans. 21. (a) As Riya covers the whole circle that means the circumference of the circle, So the total
path covered by Riya is 2πr
Distance = 2 × π × 21 = 132 cm
(b) We know that the displacement is the shortest path covered between the initial and
final point. As the initial and final points are the same,the displacement will be 0 in this
case.
OR
(c) The displacement is always less than or equal to 1,it can't be more than 1 in any case.
Displacement can be zero as well while distance can’t be zero.
The ratio of displacement to distance will always be less than or equal to 1.
oo
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Answers Worksheet - 2
Chapter - 1 (Motion)
Ans. 1. (a) Zero
Ans. 2. (c) 48 km/hr
Ans. 3. (c) 10 × 2½
Ans. 4. (b) 12 m/s
Ans. 5. Displacement is zero as it comes back to its initial point.
Now average velocity is equal to total displacement/total time. Since displacement is zero,
average velocity is also zero.
Ans. 6.
Speed
Velocity
Speed is the distance travelled by an object Velocity is the displacement of an object per
per unit time.
unit time.
It does not have any direction, thus it is a It has a unique direction, thus it is a vector
scalar quantity.
quantity.
The speed of an object can never be negative. The velocity of an object can be negative,
At most, it can become zero.
positive, or equal to zero.
Ans. 7. Initial velocity (u) = 0 (since the car is starting from rest)
Final velocity (given) (v) = 40 km h–1 = 11.11 ms–1 (convert into m/s)
Total time taken (t) = 10 min = 600 sec
v − u 11.11 − 0
We know that a =
=
= 0.0185 ms–2
t
600
Hence, the acceleration of the car is 0.0185 ms–2.
Ans. 8. The initial speed of the car (u) = 90 km h–1 = 25 ms–1
The final speed of the car (v) = 0 m s–1 (since it comes to rest)
Acceleration (a) = – 0.5 m s–2
Using the third equation of motion
v2 = u2 + 2as
(0)2 = (25)2 + 2(–0.5)s
0 = 625 – s
s = 625 m
Therefore, the car stops (1000 – 625) = 375 m before the block.
Distance
Ans. 9. We know,
Speed =
Time
Distance = 2πr = (2)(3.14)(52350 × 103) = 328758 km
Time = 20 hours
328758
Speed =
= 16437.9 km/h
20
Ans. 10. Physical quantities defined with both magnitude and direction are called vector quantities.
They should also satisfy the law of vector addition. Examples : Velocity, acceleration, force,
displacement, momentum, weight, torque, electric field, magnetic field, etc.
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Ans. 11. Physical quantities having only magnitude are called scalar quantities. Examples: Mass,
time, distance, speed, work, power, energy, electric charge, area, volume, density, pressure,
electric potential, temperature, etc.
Ans. 12. The walls of our classroom are at rest with respect to the ground or earth. But, they are in
motion with respect to an object or an observer outside the earth. This is because the earth
is moving about its own axis as well as it is revolving around the sun. Thus, the state of rest
and motion are not absolute, they are relative terms.
Ans. 13. (a) Given :
Initial velocity u = 0
v =?
a = 0.1 ms–2
t = 120 sec
v−u
a =
t
v−0
120
v = 12 ms–1
0.1 =
(b) Given that
u =0
v = 12 ms–1
t = 120 sec
a = 0.1 ms–1
According to the third equation of motion,
v2 – u2 = 2as
2
(12) – (0)2 = 2(0.1)s
144 = 0.2s
144
s =
0.2
s = 720 m
Ans. 14. (a) Initial velocity of stone (u) = 5 ms–1
Final velocity of stone (v) = 0 ms–1
(since at the maximum height, the stone comes to rest)
Acceleration (a) = 10 ms–2
Using the first equation of motion,
v = u + at
0 = 5 + (–10) t
(because the acceleration is in the opposite direction to the motion)
0 = 5 – 10t
t = 0.5 s
(b) Using this answer in the second equation of motion,
1
s = ut + at 2
2
1 2
s = (5 × 0.5)
ut++ at
× (– 10) × (0.5)2
2
s = (2.5) – (1.25)
s = 1.25 m
Thus, the maximum height attained by stone is 1.25 m.
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Ans. 15.
v
a
v = +ve; a = –ve
v
a
v = –ve; a = +ve
(a) Yes, the car’s acceleration will have a negative value.
(b) We begin with the meaning of the term “decelerating”, which has nothing to do
with whether the acceleration ‘a’ is positive or negative. The term means only that the
acceleration is opposite to the velocity and indicates that the moving object is slowing
down. One possibility is that the velocity of the car points to the right (the positive
direction) and acceleration points opposite i.e., to the left (the negative direction).
Another possibility is that the velocity of the car points to the left (the negative
direction) and acceleration points opposite i.e., to the right (the positive direction).
Ans. 16. (a) Given: Diameter of circular track, 2r = 200 m
22 diameter
22 200 4400
×
=2×
×
=
m
Circumference of circular track = 2 × π × r = 2 ×
7
2
7
2
7
Round completed by the athlete in 2 min 20 sec =
Therefore, the total distance covered =
X
140
= 3.5
40
4400
× 3.5 = 2200 m
7
r
Y
D = 200 m
Final position of athlete
XY = Diameter of circle = 200 m
(b) Since one complete round of circular track needs 40 s, so he will complete 3 rounds
in 2 mins and in next 20 s, he can complete half round.
Therefore, displacement = diameter = 200 m
Ans. 17. (a)
The displacement is a vector quantity. It is the difference between final and initial position.
When a car travels from one position to another and came back to its starting point. The
displacement is zero for that car because the difference between final position and initial
position which are at same position is zero.
Displacement = Final position – Initial position
Thus, the reason gives correct explanation for the given assertion.
Ans. 18. (b)
Speed and velocity are not same but similar quantities. The speed is a scalar quantity
and the velocity is a vector quantity. The velocity gives the direction in addition to the
magnitude of motion of an object. whereas speed gives only the magnitude but not the
direction.
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The average velocity of the fly can be determined as it is moving at uniform rate.
One can determine average speed with total distance and time taken.
Thus, assertion and reason are correct but reason does not explain the assertion as both
speed and velocity are not the same but similar quantities.
Ans. 19. Coin is flipped → coin moves in upward direction → coin experiences velocity → after
sometimes the velocity of the coin reduces → then coin reaches maximum height → where
the velocity becomes zero → coin starts to fall → coin crosses the point it is tossed →
falling coin stops moving when it reaches ground → This line should come with when coin
moves in upward direction, only then the acceleration is opposite to the direction of motion
(velocity).
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. A man sitting in a train at rest → watches a moving train in track beside → the train is
moving towards the man and moving to his back → the man feels like he is moving
in forward direction → the train in in stationary frame → the other train is in moving
frame → the man experiences relative velocity even when he is at rest to the man → the
man feels like he is moving in backward direction → the man is in the frame which is
stationary → the train is in the frame which is in motion → the observer experiences
relative velocity even when he is at rest.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) As seen from the graph, the car moves with a constant velocity which results in zero
acceleration. From B to C the object has zero acceleration.
(b) We know
a = (v– u)/t
Where
v = final velocity
u = initial velocity
a = acceleration
t = time
t = 2 sec
v = 12 m/s
u = 8 m/s
a = 12–8/2
a = 2 m/s2.
(c) Area of v – t graph represents distance of the body
Distance of the body in 6 sec is = Area of triangle (ABE) + area of rectangle (BCFE)
1 2
ut =+ (3
at × 8) + (2 × 8)
2
= 12 + 16
= 28 m
OR
(d) The total distance covered by the car can be calculated as the Area of triangle (ABE) +
Area of rectangle (BCFE) + area of trapezium (CFDG)
1 2
1 2
Total distance
ut =+ (3
at × 8) + (2 × 8)
ut ++ at
(8 +12) × 2
2
2
= 12 + 16 + 20
= 48 m
oo
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Answers Worksheet - 3
Chapter - 1 (Motion)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(a)
(b)
(c)
(b)
66 km/hr
Speed
A body moving with constant speed in a circular path
28 m/s
Distance
It is defined as the actual path traversed by
a body.
It is a scalar quantity.
It can never be negative or zero.
The distance can be equal to or greater than
displacement.
Displacement
It is the shortest distance between two
points through which the body moves.
It is a vector quantity.
It can be negative, zero or positive.
Displacement can be equal to or less than
distance.
Ans. 6. No, the displacement and the distance are not same. This is because the displacement is the
change of position of the object in motion while distance is the length of the path travelled
by it. Here, the distance travelled = 2 m while, the displacement = 0, because starting and
ending position of honey bee are same.
Ans. 7. (a) Here, displacement and velocity (average and instantaneous) both are positive.
(b) Here, displacement is positive. Instantaneous velocity is negative and average velocity is
positive.
Ans. 8. An object moving with a constant acceleration will slow down if the acceleration is
opposite to the velocity. However, if the acceleration remains constant the object will never
come to a permanent halt. As time increases the magnitude of the velocity will get smaller
and smaller. At some time, the velocity will be instantaneously zero. An instant after the
velocity is zero, the magnitude of the velocity will begin increasing in the same direction as
the acceleration. As time increases, the velocity of the object will then increase in the same
direction as the acceleration. In other words, if the acceleration truly remains constant, the
object will slow down, stop for an instant, reverse direction and then speed up.
Point of reversal
u-Velocity decreases
v=0
Velocity increases
Constant acceleration
acting in object
Ans. 9. (i)
(ii)
(iii)
Ans. 10. (i)
The difference between the highest and the lowest values of each quantity.
The intermediate values of each quantity to mark the values on the graph.
To utilise the maximum part of the paper on which graph is to be drawn.
Decelerated motion from A to B because the direction of velocity and acceleration is the
opposite. So velocity decreases.
(ii) Accelerated motion from B to C because the direction of velocity and acceleration is
same (downward). So velocity increases.
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B
v=0
A
C
Ans. 11. The slope of displacement time (x–t) graph gives the velocity of motion. One can find the
velocity of motion, finding the slope of x–t graph. To find the slope, (i) Select any two
points on the graph A and B, (ii) Draw a right angle triangle below the graph (ABT),
(iii) Find the length of BT and AT from the axis, (iv) Take the ratio of BT to AT . The ratio
has the units of velocity.
BT Displacement
slop =
=
= Velocity
Slope
AT
Time
x
Displacement
B
A
T
t
Time
Ans. 12. If the radius vector sweeps out equal angles in equal times, then its motion is said to be
uniform circular motion. In a uniform circular motion, speed remains constant. Linear
velocity, being a vector quantity, its direction changes continuously. The direction of
velocity is changing along the tangent at every point.
P′
Ds
O
Dq
r
P
Ans. 13. (a) The speed acquired :
Given,
Initial speed, u = 0 ms–1 (As it starts from rest)
Final speed, v = ?
Acceleration, a = 0.1 ms–2
Time, t = 2 minutes
= 2 × 60 seconds
= 120 s
Using the first law of motion,
Final velocity, v = u + at
= 0 + 0.1 × 120
= 12 ms–1
Therefore, the speed acquired by the bus is 12 ms–1
(b) The distance travelled:
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We know that,
Distance travelled, s = ut +
1 2
at
2
= 0 × 120 +
1
× 0.1 × (120)2
2
1
× 0.1 × 14400
2
= 720 m
Therefore, the distance travelled by bus is 720 metres.
Ans. 14. (a) If we suppose that distance from Abdul’s home to school = x km while driving to
school average speed = 20 kmh–1,
Displacement
Velocity =
Time
= 0 +
on his return trip,
or
20 =
x
x
, or, t =
h
t
20
Speed = 40 kmh–1
x
40 =
t′
t’ =
x
40 h
Total distance travelled = x + x = 2x
x
x 2x + x 3x
=
hr
+
=
Total time = t + t ' =
20 40
40
40
2 x 80 x
(b) Average speed for Abdul’s trip =
= 26.67 kmh–1.
=
3x 3x
40
Therefore, the average speed for Abdul’s trip = 26.67 km/hr.
Ans. 15. (a) The distance travelled by car in the first 4 seconds is given by the area between the
speed time curve and the time axis from t = 0 to t = 4 s
This area of the speed-time graph which represents the distance travelled by the car.
In order to find the distance travelled by car in the first 4 seconds, we have to count
the number of squares in the shaded part of the graph and also calculate the distance
represented by one square of the graph paper.
We will now calculate the distance represented by 1 square of the graph.
If we look at the X-axis, we find that 5 squares on X-axis represent a time of 2 seconds.
5 squares on X-axis = 2 s
1 square on X-axis = 2/5 s
...(i)
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Now, if we look at the Y-axis,
We find that 3 squares on Y-axis represent a speed of 2 m/s
Now,
3 squares on Y-axis = 2 ms–1
1 square on Y-axis = 2/3 ms–1
...(ii)
Since 1 square on X-axis represents 2/5 s and 1 square on Y-axis represent 2/3 ms-1
Therefore, Area of 1 square on graph
= 2/5 × 2/3
= 4/15 m
63 square represents distance = 4/15 × 63
= 16.8 m
Therefore, the car travels a distance of 16.8 m in the first 4 seconds.
(b) In uniform motion, the speed of car becomes constant. The constant speed is represented
by a speed time graph line which is parallel to the time axis. In the given figure, the
straight line graph from t = 6 s to t = 10 s represents the uniform motion of the car. The
part of graph representing uniform motion has been labelled AB.
Ans. 16.
As given in the figure above AB and CD are the speed-time graph for given two cars with
initial speeds 52 km/hr and 3 km/hr respectively. Distance travelled by the first car before
coming to rest = Area of DOAB
1
= × OB × OA
2
=
1
× 5 s × 52 km / hr
2
=
130
1
×5×
m
2
9
=
325
m = 36.11 m
9
=
1
× 10 s × 3 km / hr
2
Distance travelled by the second car before coming to rest = Area of DOCD
1
= × OD × OC
2
3 × 1000
1
× 10 ×
m
3600
2
25
5
1
m = 4.16 m
= × 10 × m =
6
6
2
=
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Therefore, clearly the first car will travel farther (36.11 m) than the second car (4.16 m).
Ans. 17. (a)
The negative acceleration occurs when the object is moving in the opposite direction to the
direction of its velocity.
An object experiences negative acceleration when the object is dropped. The object
experiences velocity and that kinetic energy is converted into stress when the object hits
the ground. This stress breaks the pot. Here, the pot experiences negative acceleration.
Thus, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 18. (c)
The Moon is under the gravitational force of earth. This makes the moon to revolve around
the earth.
When the Moon is in a circular motion around the earth, its direction changes each and
every second. The change in direction changes the velocity.
Thus, when an object is in a uniform circular motion, its velocity changes constantly.
Thus, if the assertion is true then the reason is false.
Ans. 19. Earth is a sphere → satellite moves around earth → the satellite is constantly under the
gravitational force of earth → satellite is in circular motion since it is moving around a
sphere → the satellite has to change the direction continuously to move in circular motion
→ the satellite experiences constant change in velocity → an object which is in circular
motion experiences constant change in velocity.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. An object is moving in a straight line → it is moving with a uniform rate → the object
experiences variable speed → the velocity is a vector quantity → the velocity is change in
displacement with respect to time → the average velocity is the arithmetic mean of initial
and final velocity → unit of velocity is m/s → the object should be in uniform motion to
find average velocity.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) A sloping line on a speed-time graph represents an acceleration.
(b) From B to C represents constant speed and zero acceleration as the line is a straight line
here.
(c) As we know the area of the speed-time graph gives the distance travelled by an object.
So,the area of trapezium + area of rectangle = distance travelled by the truck in 8 hours.
1
Area of trapezium (OABE) = × (sum of parallel sides) × h
2
1
=
× (10 + 35) × 3
2
= 67.5 km/h
Area of rectangle (BCFE) = (BE) × (BC)
= 35 × (8 – 3)
= 35 × 5
= 175 km.
Total distance travelled by the truck in first 8 hours = 175 + 67.5
= 242.5 km
OR
(c) When the final speed of a body is less than the initial speed then the rate of change in
speed is negative, and it is termed as retardation or negative acceleration.
If the rate of change in speed varies with time then the body possesses a varying
acceleration or retardation.
From the graph it is clear that; from points C to D the car has a varying retardation.
oo
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Answers Worksheet - 4
Chapter - 2 (Force and Laws of Motion)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(a) 0.2 kg
(a) 0.05 kg m/s
(b) 10000 N
(c) An unbalanced force
The roads where we use the cycle are rough and thus have friction so when we stop
paddling, there remains no force to overtake the friction so, then the kinetic friction slows
down the bicycle as it continuously decreases the forward moving force and so after some
time the cycle comes to rest. This is the reason for the slowdown of the bicycle while we
stop paddling.
Ans. 6. A car travelling on a highway at a fixed speed tends to maintain uniformity in its motion and
everything else inside the car. When a force from outside is applied to the car in motion, like a
sudden change in direction, the car will respond to this sudden change on its own, although
the passengers in the car or the objects inside it are still responding to inertia, where in their
motion will still be in a straight line. The change in direction has caused the passengers or the
objects to be thrown off. This event is explained by the first law of motion.
Ans. 7. Given :
Mass (m) = 40 kg
Normal force (F) = 520 N
Acceleration due to gravity (g) = 10 m/s2
Weight (w) = mg
= (40) × (10) = 400 N
To find : Acceleration of elevator,
F = ma
400 – 520 = (40) × (a)
– 120 = (40) × (a)
120
a = −
40
a = – 3 m/s2
2
Acceleration of elevator is 3 m/s , negative (–) sign indicates that the elevator travels
upward.
Ans. 8. When an object is not in equilibrium i.e., moving with changing speed, the net force on it is in
an unbalanced manner. So, it is called as unbalanced forces.
For example : When an apple falls from the tree, an unbalanced force equal to its weight
acting on the apple.
Ans. 9. Gravitational force is an attractive force that can be defined by Newton’s law of gravity which
states that “gravitational force between two bodies is directly proportional to the product of
their masses and inversely proportional to the square of the distance between them”. It is a
force exerted by large bodies such as planets and stars.
Example : Water droplets falling down.
Ans. 10. Given :
Mass (m) = 60 kg
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Weight (w) = mg = (60 kg) × (10 m/s2)
= 600 kg m/s2 = 600 N
Acceleration of elevator (a) = 3 m/s2 downward
To find : Force exerted by an object on the elevator’s floor.
Elevator accelerated downward at 3 m/s. Force acting downward will have plus sign and
force acting upward will have minus sign.
w – F = ma
F = w – ma
F = 600 – (60) × (3)
F = 600 – 180
F = 420 N
Force exerted by the object on the elevator’s floor = 420 N.
Ans. 11. The reason for the above statement is the revolution of Earth around the Sun. This fact forces
us to think of a force that provides necessary centripetal acceleration to drive the revolutionary
movement. This necessary force is provided by the force of attraction (gravitational) between
Earth and Sun.
Ans. 12. Given :
Acceleration (a) = 5 m/s2
Mass (m) = 1000 kg,
To find : Force (F) = ?
We know that
F =m×a
= 1000 kg × 5 m/s2
= 5000 kg m/s2
Therefore, required Force = 5000 kg m/s2 or 5000 N.
Ans. 13. Given :
Mass of first object A, m1 = 100 kg
Speed, v1 = 40 km/hr = 40 × (5/18)m/s
Mass of second object B, m2 = 75 kg.
Speed of second object, v2 = 60 km/hr = 60 × (5/18) m/s
(a) As inertia is a measure of mass, so object with mass 100 kg will have more inertia.
(b) We know,
Momentum = mass × velocity.
Momentum of first object = 100 × 40 × (5/18)
= 1111.1 kg m/s
Momentum of second object = 75 × 60 × (5/18)
= 1250 kg m/s
Therefore, the second object has greater momentum.
(c)If a negative acceleration is applied to both bodies then the body with smaller
momentum will stop first i.e., first object A.
(d) From third equation of motion, v² – u² = 2as.
Therefore, the body having higher velocity will travel a greater distance i.e., second
object B.
(e) The body having higher momentum will provide greater impulse during a collision so the
answer is object B.
Ans. 14. (a) Force exerted by the engine (F) = 60000 N
Frictional force offered by the surface of the track (f) = 4000 N
The net accelerating force of the engine = F – f
= 60000 – 4000
= 56000 N
(b) The acceleration of the train (a) :
The engine exerts a force of 60000 N on all 6 compartments
Accelerating force on the compartments (F) = 60000 N
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Number of compartments (n) = 6
Mass of the compartment (m1) =1000 kg
The mass of 6 compartments carried by the engine (m) = m1 × n
= 6 × 1000
m = 6000 kg
According to second law of Newton,
F =m×a
56000 = 6000 × a
56000
a =
6000
a = 9.33 m/s2
The acceleration of the train and the compartment (a) = 9.33 m/s2
Ans. 15. Initial velocity of the arrow (u) = 160 m/s
Final velocity of the arrow (v) = 0 (at rest)
Time taken by the arrow to come to rest (t) = 0.02s
Mass of the arrow = 8 g = 0.008 kg
According to the first equation of motion,
v = u + (a × t)
0 = 160 + (a × 0.02)
160
a =–
m/s2
0.02
a = – 8000 m/s2
To find,
Distance of penetration(s) = ?
Force exerted by the tree (F) = ?
According to the third equation of motion,
v2 – u2 = (2 × a × s)
2
(0) – (160)2 = (2 × – 8000 × s)
160 × 160
s =
2 × 8000
s = 1.6 m
The magnitude of the force,
F =m×a
= 0.008 × 8000
F = 64 N
The distance of penetration of the arrow in the tree (s) = 1.6 m
The magnitude of the force is calculated to be 64 N.
Ans. 16. Mass of the bullet (m1) = 1 kg
Velocity of the bullet (v1) = 8 m/s
The mass of the wooden board (m2) = 4 kg
Combined weight of the bullet and board (m1 + m2) = 4 + 1 = 5 kg
Velocity of the wooden block before collision (v2) = 0 m/s
To find:
(i) The velocity of the combined object (v) = ?
(ii) Momentum before the impact (p1) = ?
(iii) Momentum after the impact (p2) = ?
Total momentum before the collision (p1) = m1 v1 + m2 v2
= (1 × 8) + (4 × 0)
= 8 kg m/s
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After collision the wooden board and the bullet sticks together,
According to the law of conservation of momentum,
Total momentum before collision = Total momentum after collision
m1v1 + m2v2 = (m1 + m2)v
(1 × 8) + (4 × 0) = (5)v
v = 1.6 m/s
The total momentum after the collision (p2) = (m1 + m2)v
= 5 × 1.6
p2 = 8 kg m/s
(i) The velocity of the combined object (v) =1.6m/s
(ii) The total momentum before the impact (p1) = 8 kg m/s
(iii) The total momentum after the impact (p2) = 8 kg m/s
Ans. 17. (a)
When the brake is applied, the cycle stops. This is because the brake applies friction to the
wheels of the cycle. This friction opposes the motion of the wheel and the kinetic energy is
converted into potential energy partly and some energy is lost. This force eventually stops
the cycle.
Thus, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 18. (b)
An object remains in the state of rest or motion until it is forced to change its state. The
pendulum is in constant motion which is in a state of inertia until a force is applied to
change its state. This law is called Newton’s first law.
There is an equal and opposite reaction for every action. For example, the person firing the
gun experiences some opposite force. This is Newton’s third law.
Thus, both assertion and reason are true but reason is not the correct explanation of
assertion.
Ans. 19. Two balls of same weight → moving in the opposite direction → both the balls hit each
other → First ball exerts force on the second ball → second ball applies force on the first
ball → both the balls move in the opposite direction → for every action there is an equal
and opposite reaction → this condition cannot be illustrated properly if the size of the ball
varies.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. A motorcycle is moving → brake is applied → motorcycle slows down → but continues
to move for some distance → inability of an object to changes its state of motion is called
inertia → when the brake is applied suddenly → motorcycle stops → but the person riding
motorcycle moves forward → due to the inertia of the person.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) The soft ball will have less inertia as compared to the heavy ball and it would not hurt
the players.
The tendency of a body to oppose any change in its state of rest or of uniform motion
is called inertia.Inertia is directly proportional to the mass of the object.So heavier the
object, greater will be the inertia.As cork ball is heavy so it will hurt someone,thats
why it is not advisable to play with cork ball.
(b) A cricket fielder in the ground gradually pulls back his hand while collecting a fastmoving ball as the ball moves. By doing this, he uses less force to catch the ball over a
longer period of time, which causes less impetus on his hands and protects the fielder's
hands from injury.
OR
(c) From the second law of motion, Force can be calculated as rate of change of momentum,
(m × v )  v = a 


i.e.,
F =
t

t
F =m×a
So,If we know the mass of the ball and acceleration of the ball then we can calculate the
force by using the second law of motion.
oo
A-83
Answers Worksheet - 5
Chapter - 2 (Force and Laws of Motion)
Ans. 1. (c) Force
Ans. 2. (d) 1 m/s
Ans. 3. (b) Newton’s first law of motion
Ans. 4. (b) Inertia of motion
Ans. 5. Given :
Acceleration (a)
Force (F)
To find : Mass (m) = ?
We know that,
F
1000
= 5 m/s2,
= 1000 N,
=m×a
=m×5
1000
kg
m =
5
= 200 kg
Thus, the mass of the object is 200 kg.
Ans. 6. The tendency of a body in motion continues to remain in motion, moving with uniform velocity
and a body at rest continues to remain at rest unless acted upon by a force. This tendency of
the body is known as inertia. Newton’s first law of motion, this concept is quantified. The
word inertia comes from the Latin word ‘iners’ that means idle or lazy.
Ans. 7. Momentum is the quantity of motion of a moving body. In a basic sense, the more
momentum a moving object has, the harder it is to stop. It is represented as p.
p =m×v
Where, m is the mass of the body
v is the velocity of the body.
Ans. 8. Given :
Mass (m) = 500 kg,
Force (F) = 100 N,
To find : Acceleration (a) = ?
We know that,
Force = Mass × Acceleration
F =m×a
100 = 500 × a
100
⇒
a =
500
a = 0.2 m/s2
Thus acceleration of the vehicle is, 0.2 ms – 2.
Ans. 9. According to Newton’s third law of motion, when you pull the gun’s trigger, it forces the
bullet out of the gun, but at the same time, the gun is forced in the opposite direction of the
bullet (towards you). In order to keep the gun from flying away from you it is placed on the
shoulder.
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Ans. 10.
Contact force
Non-contact force
This force needs to touch the object in This force does not need to touch the object in
order to exert its effect.
order to exert its effect.
Example : muscular force, friction
Example : magnetic force, electrostatic force
Ans. 11. A wide tyre means a larger area. We know that pressure reduces when area increases
F
because P =
. The wide tyres reduce the pressure affected by a tractor. As a result, it
A
becomes easier to drive a tractor on a muddy surface or on a freshly ploughed surface.
Ans. 12. Given :
Mass (m) = 2 kg
F1 = 5 N
F2 = 3 N
To find : The magnitude and direction of the acceleration (a)
Net force :
F = F1 – F 2
= 5 – 3 = 2 N
The magnitude of the acceleration :
F
a =
m
F1 − F2
a =
m
2
2
a = 1 m/s2
The direction of the acceleration = direction of the net force = direction of F1
Ans. 13. The velocity of the ball changes four times.
(i) As a football player kicks the football, its speed changes from zero to a certain value.
As a result, the velocity of the ball gets changed. In this case, the force is applied by the
kick of the player.
(ii) When the ball reaches to another player, he kicks the ball towards the goal post. As a
result, the direction of the ball and its speed both gets changed. Therefore, its velocity
also changes. In this case, the force is applied by the kick of the player.
(iii) When the goalkeeper collects the ball, the ball comes to rest, i.e., its speed reduces to
zero from a certain value. Thus, the velocity of the ball changes. In this case, the force
is applied by the hands of the goalkeeper.
(iv) The goalkeeper then kicks the stationary ball towards his team player, i.e., the speed of
the ball increases from zero to a certain value. Hence, its velocity changes once again.
In this case, the force is applied by the kick of the goalkeeper.
Ans. 14. Given :
The mass of the car (m) = 1000 kg
Initial velocity of the car, u = 72 km/h = 20 m/s
Final velocity of the car, v = 20 km/h = 5.5 m/s
Time taken by the car to slow down = 6 s
From equation of motion,
v =u+a×t
( v − u)
a =
t
a =
A-85
(5.5 − 20)
6
a = –2.41 m/s2
To find the change in momentum of the car,
m × v – m × u = m(v – u)
= 1000(5.5 – 20)
= –14500 kg m/s
Magnitude of force (F) = m × a
F = 1000 × (–2.41)
F = –2410 N
(The –ve sign of acceleration, change in momentum and force suggests that force is
opposing the motion of the car).
Ans. 15. Given :
Mass of the body (m) = 80 kg
Initial velocity of the body (v1) = 7 m/s
Final velocity of the body (v2) = 10 m/s
Time interval for the body to be accelerated = 7 s
To find
(i) Initial momentum (p1)
(ii) Final momentum (p2)
(iii) Force exerted on the body (F)
(i) The initial momentum of the body (p1) = mv1
= (80 × 7) kg m/s
p1 = 560 kg m/s
(ii) The final momentum of the body (p2) = mv2
= (80×10) kg m/s
p2 = 800 kg m/s
According to the first law of motion,
v = u + (a × t)
v−u
a =
t
a =
a =
10 − 7
7
3
7
a = 0.428 m/s2
(iii) Force exerted on the body (F) = m × a
= 80 × 0.428
F = 34.24 N
Ans. 16. Given :
Final Velocity (v) = 0
lnitial velocity (u) = 20 m/s
Time (t) = 5 seconds
Acceleration (a) = ?
Using first equation of motion,
v = u + at
v–u
(0 – 20)
a =
=
t
5
a =
A-86
a = –4 m/s2
Here acceleration is negative because car is stopping or retarding.
Now using third equation of motion,
v2 = u2 + 2as
0 = (20)2 + 2 × (– 4)s
0 = 400 – 8s
–8 (s) = – 400
400
s =
8
s = 50 m
After applying the brake, car will travel 50 metre.
Ans. 17. (c)
A bullet fired at the fatal area in the human body can kill a human. The size of the bullet is
small as compared to the size of the human. This is because the unbalanced force applied to
the bullet is proportional to the mass and velocity of the bullet. The velocity is much higher
which increases momentum to a higher level.
The product of the mass and velocity i.e., momentum is directly proportional to the
unbalanced force applied. This applied force is enough to kill a human.
Thus, the assertion is true but the reason is false.
Ans. 18. (a)
When a bird flaps its wing then the bird flies. This is because the upward motion of the
wing pushes the air downward and the downward motion of the wing pushes the air
upward.
The bird does an action for which there is an equal and opposite reaction which helps the
birds to fly.
Thus, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 19. Metal box and paper box is placed → a boy is made to lift the boxes → the boy first lifts the
paper box without any difficulty → the boy later tries to lift the metal box → he cannot
lift the metal box → this shows the inertia of the boxes → heavy box has more inertia →
lightbox has less inertia → inertia of an object is determined with the mass of the object.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. A batsman hits a ball with great force → the force makes the ball to go beyond+++→ the ball
hits a spectator → this hurts the spectator → the ball is much smaller than a man → but a
ball can wound a man → because the momentum of the ball is greater → this exerts more
force on the man → the momentum is directly proportional to the applied unbalanced
force → Newton’s second law.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (i) (a) The coin possesses inertia of rest, it resists the change and hence falls in the glass.
(ii) (b) Newton’s first law of motion.
According to first law of motion, everybody tends to resist change of state whether
in rest or in when acted by an external force.
(iii) (c) Heavy coin will possess more inertia so it will fall in tumbler.
(iv) (d) Newton’s second law.
Formula for measuring force is given by Newton’s second law.
(v) (b)A body at rest remains at rest or, if in motion, reamins in motions at constant
velocity unless it is acted upon by an external unbalanced force.
oo
A-87
Answers Worksheet - 6
Chapter - 2 (Force and Laws of Motion)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(b) Net force applied to the body
(c) 2500 N
(b) 1 m/s2
(a) Newton’s first law
When a comb or a plastic ballpoint pen is rubbed on dry hair, an electric charge is produced
on it. This electric charge exerts a pull on the bits of paper. Thus, the force exerted by an
electrostatic charge is called an Electrostatic Force.
Ans. 6. Given :
Force, F = 120 N
Area, A = 3 m2
Pressure, P = ?
F
120
=
We know that,
P =
A
3
Pressure, P = 40 Nm–2
Ans. 7. Suppose we are moving on a bicycle at a certain speed. Now, if someone pushes the moving
bicycle from behind, then the speed of bicycle increases and it will move faster. On the
other hand, if someone pulls a moving bicycle from behind, then the speed of the bicycle
decreases and it will move slowly. Thus, a push or pull can change the speed of a moving
bicycle.
Ans. 8. (i) Applied Force.
(v) Air Resistance Force.
(ii) Gravitational Force.
(vi) Tension Force.
(iii) Normal Force.
(iv) Frictional Force.
(vii) Spring Force.
Ans. 9. (i) Force has both magnitude and direction.
(ii) Force can change the shape (and size) of a body.
(iii) Force can change the direction of a moving body.
Ans. 10. The total amount of motion present in a body is called its momentum. Linear momentum of
a body is equal to the product of its mass and velocity. It is denoted by p. Linear momentum
p = mv. Its SI unit is kg-m/s. It is a vector quantity and its direction is in the direction of
velocity of the body.
Ans. 11. Given :
m = 10 g = 0.010 kg
u = 0 ms–1
v = 300 ms–1
t = 0.003 s
To find : Force
m(v − u)
F =
t
A-88
0.01 (300 − 0)
0.003
F = 1000 N
Ans. 12. Force can change the shape of an object. When force is applied on a ball of dough, there
is a change in the shape of dough. Similarly, a potter changes a lump of clay into pots by
applying force. When air is filled in a balloon; the shape of the balloon changes because of
the applied force.
Ans. 13. (a) Given :
u = 3 m/s
v = 7 m/s
t = 2s
m = 5 kg
m ( v − u)
We have,
F =
t
=
Substitution of values in this relation gives,
5 (7 − 3)
F =
2
= 10 N
(b) Now, if this force is applied for a duration of 5 s (t = 5 s), then the final velocity can be
calculated by,
v = u + at
... (i)
Force(F)
Acceleration (a) =
Mass(m)
10
=2
5
On substituting the values of u, a and t in equation (i), we get
v = 3 + 2 × 5 = 13 m/s
We get the final velocity, v = 13 m/s.
Ans. 14. A careful observation of the distance-time table shows that
s ∝ t3
It is known that
For motion with uniform velocity (zero acceleration)
s = ut
i.e., s ∝t
(a) For motion with uniform acceleration
1 2
s = ut +
at
2
i.e.,
s ∝ t2
3
In the present case s ∝ t , we conclude in this case that acceleration must be
increasing uniformly with time.
(b) As
F = ma
Therefore, F ∝ a. Hence, the force must also be increasing uniformly with time.
Newton’s second law of motion describes the relationship between an object’s mass
and the amount of force needed to accelerate it. Newton’s second law is often stated as
F = ma
Ans. 15. (a) The initial velocity of the ball is 20 cm s–1
Due to the friction force exerted by the table, the velocity of the ball decreases down to
zero in 10 s. Thus,
u = 20 cm s–1
=
A-89
v = 0 cm s–1
t = 10 s.
Since the velocity-time graph is a straight line, it is clear that the ball moves with a
constant acceleration.
The acceleration (a) is
v−u
a =

 t 
0 − 20
cm / s 2
10
= – 2 cm s–2
= – 0.02 m s–2
(b) The force exerted on the ball is,
F = ma
 20 
 kg × (– 0.02 m s–2)
= 
1000 
=
= – 0.0004 N.
Ans. 16. Given :
Mass of the car = 1200 kg
(90 × 1000)
= 25 m/s.
3600
(18 × 1000)
Final velocity = 18 km/hr =
= 5 m/s.
3600
Initial velocity = 90 km/hr =
(a) To find acceleration :
By equation of motion, we get,
a =
=
( v − u)
t
(5 − 25)
4
= – 5 m/s2
Change in momentum = (m × v) – (m × u)
= m (v – u)
= 1200(5 – 25)
= – 24000 kg ms–1
(b) Magnitude of the force required,
F = ma
= 1200 × (–5)
= – 6000 N
Magnitude of the force required = – 6000 N
Negative sign shows that the force is in opposite direction.
Ans. 17. (c)
When a brick placed on the ground is kicked and it does not move, it means the frictional
force acting on the object is greater than the pushing force acting on the object. But to move
an object the pushing force should be greater than the frictional force.
Hence, if the brick has to move then the pushing force should be greater.
Thus, assertion is true but reason is false.
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Ans. 18. (d)
When the player catches the ball without pulling his/her hands back then the impact on the
player is more. This is because when the player is pulling the hands back then the rate of
momentum of the ball is reduced.
According to Newton’s second law of motion, the rate of momentum is directly proportional
to the applied unbalanced force.
When the rate of the momentum is reduced the applied unbalanced force is also reduced.
Thus, assertion is false and reason is true.
Ans. 19. A player catches a cricket ball → player never moves forward to catch the ball → players
always moves backward to catch the ball → because they are reducing the acceleration
→ which reduces the rate of change of momentum → from Newton’s second law → the
momentum is directly proportional to an applied unbalanced force.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. Fishes use fins for movement → the fins move the water for motion → backward motion
of fins move the fish forward → forward motion of fins move the fish backward → the
force given by the fins to move water is equal to the force to move the fish → the fish does
an action → water gives equal and opposite reaction → movement of fish works under
Newton’s third law of motion.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) According to Newton's third law, every action has an equal and opposite reaction.
When you push a wall,you are applying action force. In return the wall also applies
reaction force which acts on you but because the wall has more inertia i.e., more
mass,the wall doesn't move.
When you push a wall, the reaction force is the force the wall applies on you. The
reaction force is equal and opposite, true, but the part is that they act on two different
objects. The action force you apply acts on the wall, and the reaction force acts on you.
The force that keeps the wall in the same position is the force applied by the rest of the
building on the wall, which act in a way that keeps it in the same position as it was. The
wall doesn’t move because of cancellation of the forces. i.e., all the forces together add
to zero.
(b) (i) When a person swims , he pushes the water using hands backwards (Action), the
water pushes the swimmer in forward direction (Reaction).
(ii) Rockets expel gas at high velocity (Action). The downward moving gas pushes the
rocket in upward direction (Reaction).
(c) Even though the action and reaction forces are always equal in magnitude; these forces
may not produce accelerations of equal magnitudes because these action reaction
forces are acting on two different objects having different masses that’s why they are
accelerating with different magnitudes.
OR
(d) (i) They act on different objects.
(ii) They are equal in magnitude and opposite in direction.
(iii) Both forces acted on different object simultaneously.
oo
A-91
Progress Check - 1
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(a) Zero
(a) Speed
(b) F = ma
(c) Newton’s third law of motion
A body is in uniform acceleration when equal changes in velocity take place in equal
intervals of time, however small these intervals may be.
A body is said to be possessing non-uniform acceleration when unequal changes in velocity
take place in equal intervals of time, however small these intervals may be.
Ans. 6. In a circular motion, the angle subtended at the centre by an arc of the circular path of
motion is called the angular displacement (θ). It is measured in radians. One radian is that
angular displacement whose arc length is equal to the radius of the circle.
Ans. 7. If the particle is revolving in the clockwise direction then the direction of angular velocity
is perpendicular to the plane downwards. If the particle is revolving in the anticlockwise
direction, then the direction will be upwards.
Ans. 8. In a uniform circular motion, the particle experiences an force called the centripetal force.
The direction of centripetal force is along the radius towards the centre. Centripetal force is
required to move a particle in a circle.
mv 2
Fc = mac =
r
Ans. 9. The magnitude of the average velocity of an object will be equal to its average speed in the
condition of uniform velocity in a straight line motion.
Ans. 10. Displacement is zero as it comes back to its initial point.
Now, average velocity is given total displacement/total time. Since displacement is zero,
Average velocity is also zero.
Ans. 11. The reason is the frictional force.
There is a contact between the ball and the ground. The opposing force always acts against
the ball thereby stopping the movement of the ball.
Ans. 12. One Newton of force is defined as the amount of force needed to accelerate 1 kilogram (kg)
of mass at a rate of 1 metre per second square (ms–2).
1 N = 1 kg ms2
Ans. 13. (a) Initial speed, u = 90 kmh–1
(Converting it into ms–1, we know 1 km = 1000 m and 1 hour = 3600 seconds)
=
90 × 1000
= 25 ms–1
60 × 60
(b) Final speed, v = 0 (As the train stops)
Acceleration, a = – 0.5 m/s–2 (As the brakes are being applied the speed is reducing)
and,
Distance travelled, s = ? (To be calculated)
Now,
v2 = u2 + 2as
(0)2 = (25)2 + 2 × (–0.5) × s
A-92
0 = 625 – s
s = 625 m
Therefore, 625 metres is the distance travelled by the train before it is brought to rest.
Ans. 14. (a) Let us assume, the final velocity with which ball will strike the ground be ‘v’ and time
it takes to strike the ground be ‘t’,
Initial velocity of ball,
u = 0 m/s
Distance or height of fall,
s = 20 m
Downward acceleration,
a = 10 ms–2
As we know,
v2 = u2 + 2as
v2 = 2 × 10 × 20
[since v = 0]
v =
400 ms −1 = 20 ms–1
Therefore, final velocity of ball is 20 ms–1.
( v − u)
(b) t =
a
Time taken by the ball to strike =
(20 − 0) 20
=
= 2 seconds
10
10
Ans. 15. (a) The vehicle which has a higher mass will experience a greater force of impact. So the
lorry experiences a greater force of impact than a swift car.
(b) Change in momentum of lorry is equal and opposite to change in momentum of car,
i.e., both the vehicles experience the same change in momentum.
(c) Even though the forces on the swift car and the lorry are equal in magnitude, the swift
car experiences the greater acceleration because from equation of motion we can come
to a conclusion that acceleration produced is independent of the mass of the system.
(d) From Newton’s third law we can state that for every action, there will be an equal and
opposite reaction.
The lorry experiences a greater force of impact (action); this larger impact force is also
experienced by the swift car (reaction). So the swift car suffers greater damage than
the lorry. Since the acceleration of the swift car is greater, the velocity and momentum
change drops in a short time.
Ans. 16. (a) Inertia :
The tendency of a body to resist change in their state of rest or of motion is called inertia.
The two conditions are :
• An object at rest tends to stay at rest.
• An object in motion tends to stay in motion.
(b) Types of inertia
Inertia of rest : The ability of a body to resist any change in its state of rest.
Inertia of motion : The ability of a body to resist any change in its state of motion.
Inertia of direction : The ability of a body to resist any change in its state of direction.
(c) Examples of inertia in our day to day life applications
• When the bus suddenly takes a turn and we fall in the direction opposite to it.
• The car applies a sudden brake, we tend to fall forward.
• When a carpet is beaten with a stick, the dust falls down.
Ans. 17. (c)
The velocity of an object is the change in position of an object with respect to time. It doesn't
depend on mass of on object. The velocity is a vector quantity whereas speed is a scalar
quantity.
Thus, assertion is True and reason is false.
A-93
Ans. 18. (b)
The object with higher weight experiences higher inertia. Thus, the iron ball experiences
more inertia than a cotton ball.
The value of force is equal to mass times the acceleration. Thus, the force of an object
depends on the mass and acceleration of an object.
Thus, both assertion and reason are true but reason is not the correct explanation of
assertion.
Ans. 19. An object in uniform motion → in a straight line → velocity is constant with respect to time
→ when the object is in uniform motion → change in velocity is zero → when the object is
in non-uniform motion → change in velocity is not zero → the value is not zero because the
object is in different point at different time → change in velocity is given by acceleration
→ it is a vector quantity.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. Matchsticks have potassium → when the stick is stricken against rough surface → both
solid surfaces are stuck together → causes friction → kinetic energy is converted into
thermal energy → the matchstick burns → friction is a resistive force → thus, matchsticks
burns without white phosphorus.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a)Given: initial velocity (u) = 90 km/h = 25 m/s
Final velocity (v) = 36 km/h = 10 m/s
time(t) = 5 sec
Mass of truck = 1000 kg
(i) Acceleration of the truck = (v – u)/t
= – (10 – 25)/5
= – 3 m/s2
(b) As we know momentum = mass x velocity
Final momentum = Final momentum – initial momentum
= m2 × v – m1 × u
= 1000 × 10 – 1000 × 25
= 10000 – 25000
= – 15000 kg.m/s
(c) External force = mass × acceleration
F = 1000 × –3
F = – 3000 N
OR
(d) Momentum measures the 'motion content' of an object, and is based on the product of
an object's mass and velocity.
dp .
Force is the rate at which momentum changes with respect to time F =
dt
dp
dv
Note that if p = mv and m is constant, then F =
=m×
= ma
dt
dt
Ans. 22. (i) (c) SI unit of momentum is kg m/s.
(ii) (b) Kiran's suggestion is incorrect as momentum is always conserved
(iii) (d) P =150 kg m/s
Momentum, P = m × v = 75 × 2 = 150 kg m/s
(iv) (c)Rate of displacement
(v) (c) Momentum is the product of mass and velocity.
i.e., Momentum, P = m × v.
oo
A-94
Answers Worksheet - 7
Chapter - 3 (Gravitation)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(c) Attractive at all distances
(c) is least on the equator
(b) 229.5 g wt
(a) density
Gravitational force is one of the four fundamental forces of nature. This affects our actions
in everyday life such as walking, jumping, throwing a ball and so on. Also , it is responsible
for initiating the birth of stars, for controlling the entire structure of the universe and
evolution of the universe. Thus, we find that gravitational force is the most important force.
In fact, it is the weakest force among the four fundamental forces of nature.
Ans. 6. According to Newton’s third law of motion, the force with which the earth is attracted
towards the apple is equal to the force with which earth attracts the apple. However, the
mass of the earth is extremely large as compared to that of apple. So, the acceleration of the
earth is very small and is not noticeable.
Ans. 7. The acceleration due to gravity on the surface of the Moon is 1.6 m/s2.
Ans. 8. The line that joins any planet to the sun sweeps equal areas in equal intervals of time.
T1
A1
T2 A2
A1 = A2
T1 = T2
This law comes from the observations that planets appear to move slower when they are
farther from the sun than when they are nearer.
Ans. 9. The density of glass is more than water, but less than mercury. Therefore, glass floats on
mercury and sinks in water. A floating object displaces a weight of fluid equal to its own
weight. Archimedes, principle, as stated above, equates the buoyant force to the weight of
the fluid displaced.
Ans. 10. The buoyant force exerted by a fluid is equal to the weight of fluid displaced. Therefore, the
buoyant force increases as more and more volume of a solid object is immersed in a liquid.
The buoyant force is maximum when a body is completely immersed in a fluid.
Ans. 11. Pressure is given as force/area so,
Force, F = mg = 1 × 10 = 10 N
Area, A = 1 × 1 cm2 = 1 cm2 = 0.0001 m2
F  10 
 = 100000 Pa
Thus, the pressure exerted would be P =
=
A  0.0001 
or P = 105 Pa
A-95
Ans. 12. Fluid pressure increases with depth. So withstand with high pressure at depth of sea, the
diver wears metallic cover while going into the sea.
The pressure exerted by a static fluid depends only upon the depth of the fluid, the density
of the fluid, and the acceleration of gravity.
Ans. 13. A sheet of paper covers larger area as compared to a crumpled paper ball. Hence, sheet of
paper have large upward thrust due to air. As a result, sheet of paper falls slower than the
crumpled ball.
Ans. 14. (a)No, as of now, no method has been devised to shield a body from gravity because
gravity is independent of medium and it is the inherent property of each and every
matter. So the shield would exert the gravitational forces.
(b)The buoyant force on an object that is immersed in a liquid will be in a vertically
upward direction.
(c)Gravitational force is inversely proportional to the square of the distance whereas tidal
force is inversely proportional to the cube of the distance. So, as the distance between
the Earth and the Moon is smaller than the distance between Earth and Sun, the Moon
will have a greater influence on the Earth’s tidal waves.
Ans. 15. When an object is immersed in water, the water exerts an upward force on the object. This
upward force is equal to the weight of water displaced by an object is called the buoyant
force. If on completely immersing the object, the buoyant force is more than the weight of
object then object will rise and float on water. In other words, if the density of an object is
less than that of water, then the object will float on water. On the other hand, if buoyant
force, on completely immersing the object in water, is less than the weight of the object, the
object will sink in water. In other words, if the density of an object is greater than water,
then the object will sink in water.
Ans. 16. It is because camel’s feet have a large surface area, the force of their weight is distributed
over a large area of sand. The pressure produced on sand is small and hence, a camel’s feet
do not sink into the sand. On the other hand, a man’s feet have a small surface area; the
force of their weight is distributed over a smaller area of sand. The force per unit area or
pressure produced on sand is large in this case due to which a man’s feet sink into the sand
and it becomes difficult for him to walk on sand.
Ans. 17. (c)
The universal gravitational constant G is totally different from g.
FR 2
G =
Mm
The constant G is scalar and possesses the dimensions [M–1 L3T–2]
GM
0
–2
g = 2 , g is a vector and has got the dimensions M LT . It is not a universal constant.
R
So, assertion is true and reason are false.
Ans. 18. (a)
The army tank has large weight. Therefore, to avoid large pressure on the ground its weight
is disturbed throughout the tank. This is done by making the tank run on a steel track than
on wheels. The steel track reduces the pressure of the ground.
Thus, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 19. Earth attracts → all things towards it through an unseen → force of attraction. This force of
attraction is called as → gravitation or gravitational pull. You have noticed that every time
→ you throw an object upwards, it reaches a certain height and then → falls down on the
earth’s surface. The motion of the moon → around the earth is due to the centripetal force.
The centripetal force is provided by the → force of attraction of the earth. If there were no
such force, the moon would pursue a → uniform straight line motion.
[Words marked in BOLD are new information which is not mentioned]
A-96
Ans. 20. Archimedes’ principle states that → the upward buoyant force that is exerted on a body
immersed in a fluid, whether → fully or partially submerged, is equal to the weight of the
fluid that the → body displaces and acts in the upward direction at the → centre of mass
of the displaced fluid. Archimedes’ principle is a law of physics fundamental to → fluid
mechanics. It was formulated by → Archimedes of Syracuse.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) In order to be able to notice the gravitational force of attraction between any two objects,
at least one of the objects on the earth should have an extremely large mass. Since no
object on the earth has an extremely large mass, we cannot notice such forces. The
two cars in the road do not collide with each other because of their small masses, the
gravitational force of attraction between them is too weak. Also other objects present
there will also apply some forces on the two cars which ultimately cancel out the forces.
(b) As discussed by the Riya and Siya teacher,the force of gravity depends upon:
1. Mass of an object
2. Distance between the two masses.
( G × M × m)
F =
r2
Where is the mass of earth
m is the mass of an object
R is the distance between two masses.
And G is the gravitational constant whose value is 6.67 × 10–11 Nm2/kg2
OR
(c) The universal law of gravitation successfully explained several phenomena which
were believed to be unconnected :
(i) the force that binds us to the earth;
(ii) the motion of the moon around the earth;
(iii) the motion of planets around the Sun; and
(iv)the tides due to the moon and the Sun
oo
A-97
Answers Worksheet - 8
Chapter - 3 (Gravitation)
(b) Nm2kg– 2
(d) 9.8 m/s2
(c) Buoyant force does not change with depth
(c) newton
According to the universal law of gravitation, the force between two bodies is directly
proportional to their masses and inversely propertional to the square of the distance
between them. Mathematically, it is represented as follows :
mm
mm
F ∝ 12 2 ⇒ F = G 12 2
r
r
where,
F is the gravitational force between two bodies
m1 is the mass of one object
m2 is the mass of the second object
r is the distance between the centers of two objects
G is the universal gravitation constant.
Ans. 6. The law of gravitation can be applied :
(i) To find the force exerted by planets on other bodies.
(ii) To determine the motion of the planets around the sun.
Ans. 7. The acceleration due to gravity is more at the poles than at the equator. When the initial
velocities and distances travelled are the same, the time taken by the body is smaller if the
acceleration due to gravity is large. Hence, when dropped from the same height, a body
reaches the ground quicker at the poles than at the equator.
Ans. 8. The source of centripetal force, that a planet requires to revolve around the Sun is
gravitational force between planet and Sun, it depends on masses of planet and Sun and
distance between them.
Ans. 9. Given :
mass of the substance = 50 g
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
Volume of the substance = 20 cm3
Mass
Density of substance =
Volume
 50 
=   g/cm3
 20 
= 2.5 g/cm3
Since the density of the substance 2.5 g/cm3 is greater than the density of water (1 g/cm3),
so the substance will sink in water.
Ans. 10. A body can float on the surface of the water if the upthrust balances the weight of the body.
Ans. 11. The cutting edge of a knife should as sharp to create greater pressure even for a very small
applied force for quick action.
Ans. 12. Weight of cork is less than the buoyant force acting on it so it floats whereas weight of the
nail is more than the buoyant force acting on it so it sinks.
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Ans. 13. (a)
Here, Initial speed,
u =0
Final speed,
v = ? (To be calculated)
Acceleration due to gravity, g = 10 m/s2 (ball comes down)
and
Height, h = 20 m
Now, we know that for a freely falling body :
v2 = u2 + 2gh
v2 = (0)2 + 2 × 10 × 20
So,
or
v2 = 400
v = 400
v = 20 m/s
(b)
Thus, the speed of cricket ball when it hits the ground will be 20 metres per second.
Now,
Initial speed, u = 0
Final speed,
v = 20 m/s
(Calculated above)
2
Acceleration due to gravity, g = 10 m/s
and
Time, t = ?
(To be calculated)
Putting these values in the formula :
v = u + gt,
We get :
20 = 0 + 10 × t
10 t = 20
20
t =
10
t =2s
Thus, the ball takes 2 seconds to fall through a height of 20 metres.
Ans. 14. Gravity is the force by which a planet or other body draws objects toward its centre. The
force of gravity keeps all of the planets in orbit around the Sun.
Anything that has mass also has gravity. Objects with more mass have more gravity. Gravity
also gets weaker with distance. So, the closer objects are to each other, the stronger their
gravitational pull is.
Earth’s gravity comes from all its mass. All its mass makes a combined gravitational pull on
all the mass in your body. That’s what gives you weight. And if you were on a planet with
less mass than Earth, you would weigh less than you do here.
Ans. 15. Given :
Mass of packet = 500 g
Volume of packet = 350 cm3
Mass
Density of packet =
Volume
 500 
 g/cm3 = 1.43 g/cm3
= 
350 
The sealed packet will sink in the water as its density 1.43 g/cm3 is greater than that of
water.
The volume of water that will be displaced by the packet = 350 cm3
and mass of this displaced water = Volume x Density = 350 × 1 = 350 gm
Ans. 16. The tendency of a liquid to exert an upward force on an object placed in it is called buoyancy.
When a body is completely or partially immersed in a fluid, then the upward thrust acting
on the body is called the force of buoyancy or buoyant force.
It increases as we push the object deeper into water. The magnitude of this buoyant force
depends on the density of the fluid.
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Ans. 17. (b)Both assertion and reason are true but reason is not the correct explanation of
assertion.
Ans. 18. (c) Assertion is true but reason is false.
Ans. 19. An object falls from any → height under the influence of gravitational force only, it is
known as free fall. Whenever objects fall towards the → earth under this force alone, we
say that the → objects are in free fall. While falling, there is no change in the → direction
of motion of the objects. But due to the earth’s attraction, there will be a change in the →
magnitude of the velocity. Any change in velocity → involves acceleration.
[Words marked in BOLD are new information which is non mentioned]
Ans. 20. Buoyancy is the upward force → exerted by fluids over the surface area of → contact of an
object which is immersed in fluids. Buoyancy is also known as → upward thrust. When an
object is immersed in water, it exerts → pressure over water due to its weight. At the same
time water also → exerts upward thrust over the object. If the force exerted by the object
is greater than the → upward thrust or buoyancy by → water, the object sinks in water
otherwise it floats over water.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (i) (c) F = GM1M2/r2
(ii) (c) Gravitational constant, 6.67 × 10–11 Nm2/kg2
(iii) (c) 9.8N
(iv) (d)Both (b) and (c)
(v) (b)Gravitational force
oo
A-100
Answers Worksheet - 9
Chapter - 3 (Gravitation)
Ans. 1. (a)
1
F
4
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(d) Square of distance between masses.
(b) 8 g/cm3
(a) Thrust
The region around a massive body where in a force of attraction is felt by other bodies is
called a gravitational field, for e.g., an object that exists on and near the surface of the earth,
experience a force of attraction towards the centre of the earth.
Ans. 6. (i) Latitude of the place.
(ii)
Radius of the earth. Value of g is maximum at poles and minimum at equator of the
Earth.
Ans. 7. The Moon can escape only if the moon has no orbital motion. In fact, while revolving around
the Earth, the Moon has orbital motion around the Sun also. The gravitational attraction of
the Sun on the Moon provides the centripetal force required for the orbital motion around
the Sun.
Ans. 8. When an object is under free fall, its velocity changes due to gravitational force. The change
in velocity brings about acceleration in the object. This is called acceleration due to gravity.
The value of acceleration due to gravity or g = 9.8 m/s2.
Ans. 9. The instrument used to determine the density of liquids is hydrometer. It consists of a
uniform test tube. The base of the tube is made heavier by taking few lead shots in it so that
the tube remains vertical while floating in the water or a given liquid.
Ans. 10. The pressure in liquids is given by P = ρ × g × h
Where, ρ is density of liquid, g is gravity and h is the depth in the liquid.
Ans. 11. A body floating freely in a fluid, must obey the following laws known as laws of floatation:
(i)A body floats only if its weight is equal to the weight of fluid displaced by its immersed
part.
(ii)For the body to float in upright position, the centre of gravity of the floating body and
the centre of buoyancy of the fluid displaced by the immersed part of the body must lie
on the same straight line. First law stated above is necessary for the body to float where
as the second law stated above is necessary for the body to float in upright position.
Ans. 12. Conclusions drawn from the experiment are :
(i) The pressure in sand is greater when the solid iron cuboid is placed on its least surface
area.
(ii) The pressure exerted by the smallest surface area is greater than the other surfaces
with larger areas. Yes, it matches with the theoretical aspect.
Ans. 13. The two forces are:
(i) Weight of the body acting downwards.
(ii) Buoyant force acting upwards.
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Ans. 14. (a)
Density of solid =
=
Mass of solid
Volume of soild
500
350
= 1.42 g cm – 3
Thus, the density of the given solid is 1.42 g cm–3.
(b) The solid will displace water equal to its own volume. Since the volume of the solid
is 350 cm3 so it will displace 350 cm3 of water. Now, the volume of water displaced is
350 cm3 and the density of water in common units is 1 g cm–3. Putting these values for
water in the formula :
Mass of water
Density of water =
Volume of water
1 =
Mass of water
350 cm
So, Mass of water displaced is 350 grams.
_
3
Ans. 15. The principle states that : “A body immersed in a liquid loses weight by an amount equal to
the weight of the liquid displaced.” Archimedes' principle also states that : “When a body
is immersed in a liquid, an upward thrust, equal to the weight of the liquid displaced, acts
on it.” Thus, when a solid is fully immersed in a liquid, it loses weight which is equal to the
weight of the liquid it displaces. Loss in weight of solid = Weight in air – Weight in liquid
Loss in weight of solid = the weight of the liquid displaced. The more the density of liquid
in which the solid is immersed, the less is the weight of the liquid displaced on immersing
the solid.
Ans. 16. When an object is placed on the surface of the water, two forces act on the object :
(i) The gravitational force in the downward direction.
(ii) Upthrust or buoyant force in the upward direction.
When the gravitational force is greater than the upthrust or buoyant force on the object,
the object sinks in water. If the upthrust or buoyant force is greater than or equal to the
gravitational force, then the object floats.
Ans. 17. (a)
Inertial mass and gravitational mass are equivalent. Both are scalar quantities and measured
in the same unit.
They are quite different in the method of their measurement. Also, the gravitational mass
of a body is affected by the presence of other bodies near it whereas internal mass remains
unaffected.
So, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 18. (b)
The force acting normally (perpendicular) on a surface is called thrust. The thrust is a vector
quantity and is measured in the unit of force. Both statements are correct but the reason is
not the correct explanation for the given assertion.
Ans. 19. Acceleration due to gravity is simply the → acceleration produced in a body because of the
→ gravitational force (pull) of the earth. Acceleration due to gravity is a → vector quantity,
which means it has both → magnitude and a direction. The acceleration due to gravity at
the → surface of Earth is represented as g.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. Buoyancy is the upward force → exerted by fluids over the surface area of → contact of an
object which is immersed in fluids. Buoyancy is also known as → upward thrust. When an
object is immersed in water, it exerts → pressure over water due to its weight. At the same
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time water also → exerts upward thrust over the object. If the force exerted by the object
is greater than the → upward thrust or buoyancy by → water, the object sinks in water
otherwise it floats over water.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) No,they are different.Mass is the amount of "matter" in an object (though "matter" may
be difficult to define), whereas weight is the force exerted on an object by gravity.
(b) The weight of an object is the force with which it is attracted towards the earth, the SI
unit of weight is the same as that of force, that is, Newton (N). The weight is a force
acting vertically downwards; it has both magnitude and direction.
W=m×g
SI unit is Newton(N).
1
(c) Weight of the object on the moon =   × its weight on the earth.
6
So,according to the question,weight of Janvi on earth is 60 N which will become 1/6th
on the moon. i.e., 10 N
1
Weight of Manvi on the earth is 48 N which will become th on the moon i.e., 8 N.
6
OR
(d) The weight of an object on moon is 30 N. So on the earth its weight will be 6 times. i.e.,
180 N.
oo
A-103
Answers Worksheet - 10
Chapter - 3 (Gravitation)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(a) Principle of flotation
(a) N/m2
(c) Inertia
(d) Satellite
To reduce the area and hence to increase the pressure for the given force the needles have
sharp edge.
Ans 6. The two forces are :
(i) Weight of the object acting downwards.
(ii) The buoyant force acting upwards.
The upward force that tends to lift the body is called the buoyant force. The buoyant force
acting on floating and submerged objects can be estimated by employing hydrostatic
principle. This result shows that the buoyant force acting on the object is equal to the weight
of the fluid it displaces.
Ans. 7. Fluid is a substance that flows. For example, liquids, and gases. They take the shape of
container in which they are stored. The study of fluids at rest is known as hydrostatic or
fluid statics. The study of fluids in motion is termed as hydrodynamics.
Ans. 8. Yes, this statement could be true. The pressure is inversely related to the area over which
force distributed. The clown on stilts is exerting force over a much smaller area than the
two clowns setting on the ground. He is exerting twice as much pressure as the other two
clowns are.
Ans. 9. Any change in the distribution of the Earth’s mass will not affect the variation of acceleration
due to gravity with height. This is because, for a point outside the earth, the whole mass of
the earth is effective and the earth behaves as a homogeneous sphere.
Ans. 10. All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse.
This law was a deviation from the Copernican model which allowed only circular orbits.
The ellipse, of which the circle is a special case, is a closed curve which can be drawn very
easily.
Ans. 11. Due to air friction, the satellite loses a part of its total energy and the satellite comes closer
to earth’s surface. Thus, it loses height. When they enter into denser region of the earth’s
atmosphere, the heat generated causes them to burn out.
Ans. 12. The value of g is largest at the poles due to the following two reasons :
(i) The distance of poles from the centre of earth is smaller than the distance of any other
point on the earth’s surface from its centre.
(ii) At poles, no centrifugal force acts on the body.
Ans. 13. A submarine can both sink and float on water because of the ballast tank.
To make a submarine sink into the water, these tanks are filled with water. This increases
the weight of the submarine and it sinks.
To make a submarine float on the water surface, these tanks are emptied by pumping out
water from them. This decreases the weight of the submarine and it floats on water surface.
Ans. 14. Mass doesn’t change with position while weight changes with position because mass is
inertial property of matter and doesn’t depend on any of the factor while weight is depends
on gravitational acceleration, which varies at different places like on Earth it is g and on
Moon it is g/6.
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Ans. 15. Yes, you weigh less on the equator than at the North or South pole, but the difference is
small. Note that your body itself does not change. Rather it is the force of gravity and other
forces that change as you approach the poles. These forces change right back when you
return to your original latitude.
Ans. 16. When it comes to the fundamental laws of nature, we can break everything down into four
forces that are at the core of everything in the Universe :
The strong nuclear force : The force responsible for holding atomic nuclei and individual
protons and neutrons together.
The electromagnetic force : The force that attracts and repels charged particles, binds
atoms together into molecules and causes electric current, among other things.
The weak nuclear force : The force responsible for some types of radioactive decay and the
transmutation of heavy, unstable fundamental particles into lighter ones.
Gravity : The force that binds the Earth, the solar system and the stars and galaxies together.
Ans. 17. (a)
Both assertion and reason are true and reason is the correct explanation of assertion.
As gravitational force on the Earth is higher than that on the Moon hence mountains will
have lower height on the earth.
Ans. 18. (c)
Acceleration due to gravity is given by.
GM
g = 2
R
Thus, it does not depend on mass of the body on which it is acting. Also, it is not a constant
quantity, it changes with a change in the value of both M and R (distance between two
bodies).
So, the assertion is true but reason is false.
Ans. 19. Force exerted by an object → perpendicular to the surface is called thrust. Force exerted by
an object → per unit area is called pressure. For example, you stand on loose sand. Your
feet go deep into the sand. Now, lie down on the sand. You will find that → your body will
not go that deep in the sand. In both, the cases → force exerted on the sand is the → weight
of your body. You have learnt that → weight is the force acting vertically downwards. Here
the force is acting → perpendicular to the surface of the sand. The force acting on an object
is → perpendicular to the surface is called thrust.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. Every object attracts the → other object by a → force of attraction in the universe, is called
→ gravitation, which is directly proportional to the → product of masses of the objects and
inversely proportional to the → square of the distance between them. This is called → Law
of Gravitation or Universal Law of Gravitation. The law is universal in the sense that it
is → applicable to all the bodies, whether the bodies are big or small, whether they are →
celestial or terrestrial.
[Words marked in BOLD are new information which is not mentioned]
oo
A-105
Answers Worksheet - 11
Chapter - 3 (Gravitation)
(a) kg m–3
(a) Finding purity of milk
(b) That every body in the universe exerts a gravitational force on every other body.
(a) Is opposite to the direction of motion.
The tides in the sea formed by the rising and falling of water level in the sea are due to the
gravitational force of attraction which the sun and the moon exert on the water surface in
the sea.
Ans. 6.
10 small divisions = 25 g/1 small divisions
25
=
= 2.5 g wt.
10
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
Least count of spring balance = 2.5 g wt.
Ans. 7. The mug appears lighter as the buoyancy force acts in the upward direction which reduces
the effective weight of mug when placed in water.
F
Ans. 8. P =
A
250 =
A=
50
A
50
250
A = 0.2 m2
Ans. 9. Tides are formed by a combination of the gravitational pull of the Moon exerted on earth
and to a lesser extent, the Sun. The oceans on earth bulge towards the Moon because this is
where gravity is the strongest. On the opposite side of the Earth, the gravitational attraction
of the Moon is less.
Ans. 10. The gravitational constant, called G in physics equations, is an empirical physical constant.
It is used to show the force between two objects caused by gravity. The gravitational
constant appears in Newton’s universal law of gravitation. G is about 6.67408 × 10–11
N-m2/kg2 and is denoted by letter G.
Ans. 11. The astronaut and the spaceship are orbiting with same acceleration hence, the body does
not exert any force on the sides of the spaceship. Therefore, the body appears to be floating
weightlessly. It also implies that a body orbiting in space has zero weight with respect to a
spaceship.
Ans. 12. Due to the small value of ′g′, the escape velocity on the Moon surface is small (2.38 km s-1).
The air molecules have thermal velocities greater than the escape velocity. Therefore, the air
molecules escape away and cannot form atmosphere on the Moon.
Ans. 13. (i)The planets move in elliptical orbits around the Sun, with the Sun at one of the two foci
of elliptical orbit.
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(ii)Each planet revolves around the Sun in such a way that the line joining the planet to
the Sun sweeps over equal areas in equal intervals of time.
(iii)The cube of the mean distance of a planet from the sun is directly proportional to the
square of time it takes to move around the Sun. i.e., r3 ∝ T2.
Ans. 14. Archimedes’ principle states that when a body is immersed partially or fully in a fluid, it
experiences an upward force that is equal to the weight of the fluid displaced by it.
The two applications of Archimedes' principle are given below :
(i) Floating of ships and submarines.
(ii) The lactometers to test the purity of milk.
Ans. 15. (a)It is due to force of gravitation between planet and Sun. This gravitational force
balances the centripetal force of planetary motion. Therefore, planet revolve around
the Sun in fixed orbit.
(b)It is due to force of gravitation among Moon, Earth and Sun. When Moon and Sun
both are in same direction it exerts more force of gravitation on Earth which causes
occurrence of tides as maximum part of Earth is covered by the water.
Ans. 16. Mass and weight are closely related because mass affects the weight of an object
experiencing the effects of gravity. Weight is the measure of the force of gravity on an
object’s mass, while mass is the measure of how much matter there is in an object.
An object’s weight is calculated as the mass of an object in kilograms multiplied by the
acceleration of gravity exerted in metres per second square. The resulting number is
expressed in Newton’s, named for Newton’s second law of motion. An object’s mass is
determined by comparing it to an object with a known mass on a balance. An object with a
mass of 1 kilogram would weigh 9.8 N on Earth, yet it would weigh essentially nothing in
space while still having a mass of 1 kilogram.
Ans. 17. (c)
GM
Acceleration due to gravity is given by by g =
. Thus, it does not depend on mass of
R2
body on which it is acting. Also it is not a constant quantity, it changes with change in value
of both M and R (distance between two bodies). Here, both assertion and reason are false.
Ans. 18. (a)
As the rotation of earth takes place about the polar axis, therefore, the body placed at poles
will not feel any centrifugal force and its weight or acceleration due to gravity remains
unaffected.
So, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 19. The density of a substance is defined as → the mass of a unit volume. The unit of density is
→ kilogram per metre cube. The density of a given substance, under specified conditions,
remains the same. Therefore, the density of a → substance is one of its characteristic
properties. It is different for → different substances. It is often convenient to → express the
density of a substance in comparison with that of water.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. The mass of a body is the → quantity of matter contained in it. Mass is a scalar quantity
which has only → magnitude but no direction. Mass of a body always remains → constant
and does not change from place to place. Mass of a body can never be → zero. The force
with which an object is → attracted towards the centre of the earth is called the → weight of
the object. As weight always acts → vertically downwards, therefore, the weight has both
→ magnitude and direction and thus it is a vector quantity.
[ Words marked in BOLD are new informations which is not mentioned].
oo
A-107
Answers Worksheet - 12
Chapter - 3 (Gravitation)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
(b)
(d)
(a)
(a)
Making the area half
Friction force
Gravitational force
G
Ans. 5.
Density of body =
=
M
V
400
300
= 1.3 gm/cm3
which is greater than the density of water 1 gm/cm3. Hence, body will sink in water.
Ans. 6. It is difficult to hold a school bag having a strap made of a thin and strong string because
it applies the large pressure on the shoulders due to very small contact surface area . We
know that the pressure is inversely proportional to the surface area on which the force acts.
Ans. 7. The weighing machine reads slightly less than the actual value. This is because of the
upthrust of air acting on our body.
Hence, our actual weight is more than 42 kg.
Ans. 8. Both iron and cotton are weighing same, however, there is a large buoyant force on cotton
bag because of its area. Therefore, it feels to weigh less.
Ans. 9. When an object falls freely towards the surface of earth from a certain height, then its
velocity changes and this change in velocity produces acceleration in the object which is
known as acceleration due to gravity denoted by g. The value of acceleration due to gravity
is 9.8 ms–2.
Ans. 10. The value of ‘g’ at the equator of the earth is less than that at poles. Therefore, the packet
falls slowly at equator in comparison to the poles. Thus, the packet will remain in air for a
longer time interval, when it is dropped at the equator.
Ans. 11. Due to rotation of the Earth about its polar axis, every particle on the earth has a linear
velocity directed from west to east. This velocity (v = R × w) is maximum at the equator.
When a rocket is launched from west to east, this maximum velocity gets added to the
launching velocity, so the launching becomes easier.
Ans. 12. Escape velocity is referred to as the minimum velocity needed by any body or object to
be projected to overcome the gravitational pull of the planet Earth. In other words, the
minimum velocity that one requires to escape the gravitational field is escape velocity.
Ans. 13. The pressure (P) is defined as the magnitude of the normal force acting on a unit surface
area of the fluid. Hence pressure is indirectly proportional to area of contact.
P=
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F
A
For example, a nail or a knife have pointed and sharp edge to reduce the area of contact to
apply large pressure.
S.I. unit of pressure is Nm–2 or pascal (Pa). The unit of pressure, pascal (Pa) has been named
in the honour of great French scientist and philosopher Blaise Pascal.
Another unit of pressure is atmosphere (atm).
1 atm = 1.013 × 105 Nm–2(or Pa)
1 atm or one atmosphere is the pressure exerted by our atmosphere on Earth surface due to
the weight of atmosphere.
The pressure is a scalar quantity. This is because pressure is transmitted equally in all
directions when force is applied, which shows that a definite direction is not associated
with pressure.
Ans. 14. Weight of liquid inside the vessel = volume × density of liquid × acceleration due to gravity
Thrust of liquid = weight of liquid = mass × gravitational acceleration = d × v × g
Buoyant force = Weight of fluid displaced = Vρg
Where V = volume of fluid displaced [m3], ρ = density of fluid [kg m–3], g = gravitational
acceleration [ms–2].
Hence, we can conclude that :
• The liquid at rest exerts equal pressure in all directions at a point inside the liquid.
•Total pressure at a depth h below the liquid surface = P + hdg where d is density of
liquid, P = atmospheric pressure.
• Liquid pressure is independent of shape of the liquid surface but depends upon the
height of liquid column.
Ans. 15. The heart is not strong enough by itself to get the blood back up the veins in your legs
and back to your heart. The human body relies on a second system to finish that task.
This system involves small valves throughout the veins and muscle contractions from your
skeletal muscles when you walk and move about. The valves close when blood starts to
flow in one direction, so that blood in the veins can only flow in the direction back to the
heart, which is above the legs. When you squeeze your leg muscles to walk, stand, kick,
and move about, the muscles squeeze the veins and force the blood to get moving. Because
of the valves, the blood can only move in one direction as it gets squeezed along. So it is
a combination of blood pressure from the heart’s pumping action, the valves, and muscle
movement that gets the blood up the legs against gravity.
Ans. 16. Force acting on a moving body at an angle 90° to the direction of motion, tending to make
the body follow a circular or curved path is called centripetal force. The force of gravity
acting on a satellite in orbit is an example of a centripetal force; the friction of the tyres of a
car making a turn similarly provides centripetal force on the car.
In a popular carnival ride, people stand with their backs against the wall of a cylindrical
chamber. The chamber spins rapidly, the floor drops out, but the riders remain pressed
against the wall without falling. Although the riders may insist they stay aboard because of
an outward force pushing them against the wall, the reality is the opposite: the riders are
subject to an inward, or centripetal force. As the ride spins, it forces the riders to travel in a
circle.
Ans. 17. (a)
Both (A) and (R) are true and (R) is correct explanation of the assertion.
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Ans. 18. (c)
A person feels his weight only when the surface on which he is standing exerts a reactionary
force on him. Because the acceleration of the person and that of the satellite revolving
around the earth are equal (= g), hence the downward acceleration of the person with
respect to the satellite is zero. Therefore, a person feels weightless on satellite, although the
gravitational force is acting on a satellite.
So, the assertion is true but reason is false.
Ans. 19. The gravity of Earth, denoted by g, is the → net acceleration that is imparted to objects
due to the combined → effect of gravitation (from distribution of mass within Earth) and
the → centrifugal force (from the Earth’s rotation). The precise strength of → Earth’s gravity
varies depending on location. The nominal “average” value at → Earth’s surface, known
as standard gravity.
[Words marked in BOLD are new information which is not mentioned]
oo
A-110
Answers Worksheet - 13
Chapter - 3 (Gravitation)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(c) Remains constant
(a) Faster
(b) 997 kg/m3
(c) Area
The force of attraction between two objects depends on the product of masses of the two
objects. Hence, the force of attraction between two objects is constant for a given distance
between them. So, both the Earth and the Moon would attract each other with equal force.
Ans. 6. The collision between the two satellites is inelastic. They stick together mv + (− mv)
= (m + m)V or V = 0. The kinetic energy of the debris in its orbit will be zero. Due to gravity,
it falls to the surface of the Earth and in the course of its journey, it may get burnt up.
Ans. 7. The universal law of gravitation helps in explaining many phenomena. Some of them are
as follows :
• We keep on remaining on the earth’s surface.
• The earth moves around the sun.
• The planets and their satellites remain in their respective orbits.
• The tides happen at regular intervals.
Ans. 8. As we go inside the Earth, the value of attracting mass M decreases and its value becomes
zero at the centre of the Earth. Consequently, a body at the centre of the Earth feels no
gravitational attraction or its weight becomes zero at the centre of the Earth.
Ans. 9. The specific gravity of a substance is defined as the ratio of density of a substance to the
density of water (for solids and liquids) and hydrogen (for gases).
Ans. 10. To reduce the area and hence to increase the pressure for the given force.
Ans. 11. Due to the upthrust exerted by the well water on the bottom of the bucket in an upward
direction.
Ans. 12. Here,
area (A) = 0.5 m2, pressure (P) = 50 Pa
we know that,
Force (F) = P × A
= 50 × 0.5
= 25 N
Ans. 13. There are two kinds of accelerations, rotational and linear. A ship could achieve artificial
gravity by rotating about its axis to be practical, the radius of rotation would have to be
quite large. Additionally, a ship could create artificial gravity by constantly accelerating
forward.
Ans. 14. Newton’s law of universal gravitation states that every particle attracts every other particle
in the universe with a force which is directly proportional to the product of their masses
and inversely proportional to the square of the distance between their centres. The universal
law of gravitation must be applicable to any pair of bodies.
Ans. 15. We know that,
F = mg (Gravitational force acting on any object)
From Newton’s universal law of gravitational force between object of mass m and earth
with mass M is given by
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F =
GMm
R2
mg =
GMm
R2
g =
GM
R2
g =
6.67 × 10 −11 × 6 × 10 24
(6.4 × 10 6 )2
= 9.8 m/s2
Ans. 16. Here, Volume of sphere = Volume of water displaced = 2.2 × 10–4 m3
..
( . sphere is completely immersed in water)
Mass of the water displaced = Volume × Density = 2.2 × 10–4 m3 × 1000 kg m–3
= 0.22 kg
Thus, buoyant force exerted by water = weight of water displaced = mg
= 0.22 kg × 9.8 m/s2
= 2.156 N.
Ans. 17. (a)
We know that the weight of an object on the Earth is six times the weight of the object on
the Moon. The weight of an object on the Earth is the force with which the Earth attracts
that object whereas the weight of an object on the Moon is the force with which the Moon
attracts the same object. The attractive force of the Moon is lesser than the attractive force
of the Earth due to fact that the mass of the Moon is lesser than the mass of the Earth. Thus,
both assertion and reason are true and reason gives the correct explation of assestion.
Ans. 18. (c)
We can hear the sound of thunder after the lightning occurs. It is because the speed of the
sound is slower than the speed of light. The speed of the sound depends on the medium
which travels through it and also directly proportional to the temperature and pressure of
the medium. Thus, the given assertion is true but the reason is false.
Ans. 19. Weight of an object on the Moon is the → force with which the object is attracted by the
Moon. The mass of the Moon is → less than that of the Earth. So the force exerted by the
→ Moon on an object is also less. The value of → ‘g’ on the Moon is only about one-sixth
of that on the Earth. So a body weight → one-sixth of the moon than on the Earth, though
its → mass is the same on the Moon as on the Earth.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. When water is drawn from a well with a → bucket tied to a long rope. It is easy to → lift
the bucket when it is immersed in water. But as soon as it is out of water, it → suddenly
appears to be heavier. When a body is → partly or completely immersed in a fluid, it
experiences an upward → force from the liquid displaced, which is called buoyant force.
[Words marked in BOLD are new information which is not mentioned]
oo
A-112
Answers Worksheet - 14
Chapter - 4 (Work and Energy)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(c) Energy
(c) Kinetic energy
(a) joule
(d) All of these
Work is defined as a force causing the movement or displacement when force is applied on
a body. The S.I. unit of work is joule (J).
Ans. 6. The measure of energy transfer that occurs when an object is moved over a distance by an
external force which is applied in the direction of the displacement.
Ans. 7. One joule is defined as the amount of energy exerted when a force of one newton is applied
over a displacement of one metre. One joule is the equivalent of one watt of power radiated
or dissipated for one second. In some applications, the British thermal unit (Btu) is used to
express energy.
Ans 8. 1 unit of energy is equal to 1 kWh.
1 unit = 1 kWh
1 kWh = 3.6 × 106 J
Therefore,
250 units of energy = 250 × 3.6 × 106
= 9 × 108 J
Ans. 9. Work is done whenever the following conditions are satisfied :
(i) A force acts on the body.
(ii) There is a displacement of the body caused by the applied force along the directions of
the applied force.
Ans. 10. Whenever work is done a force moves something over a distance. You can calculate the
energy transferred, or work done, by multiplying the force by the distance moved in the
direction of the force.
Energy transferred = work done = force × distance moved in the direction of the force.
Ans. 11. Power is the rate of doing work or of transferring heat, i.e., the amount of energy transferred
or converted per unit time.
Work
Power =
Time
Ans. 12. The SI unit of power is the watt (W), which is equal to one joule per second.
Ans. 13. (a) Formula for work done is given as :
W =F×s
(b) Mass of car, m = 1000 kg
Initial velocity, u = 20 m/s
Final velocity, v = 10 m/s
Work done, W = ?
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Using third equation if motion
v2 – u2 = 2as
102 – 202 = 2as
as = – 150
...(i)
Work done, W = F × s
But
F =m×a
So,
W =m×a×s
Put the value of 'as' from equation (i),
W = 1000 × (– 150) = – 150000 = – 150 kJ
Neagtive sign implies that force of brakes acts opposite to the direction of motion.
Ans. 14. (a) The energy possessed by a body by virtue of its position relative to others, stresses
within itself, electric charge, and other factors.
Formula,
P.E. = mgh
(b) PEtop = KEbottom
Using the equations for potential and kinetic energy, we can solve for the height of the
hill.
1
2
mgh = mv
2
The masses cancel and we can plug in our final velocity and gravitational acceleration.
1
gh = v 2 ,
2
(c)
Ans. 15. (a)
Putting,
v = 12 m/s, g = 9.8 m/s2
and
h = 7.35 m
Potential energy and work done are the same thing.
Energy which a body possesses by virtue of being in motion.
1
Formula,
K.E. = mv 2 .
2
(b) Given :
Mass of the body, m = 250 kg
Velocity, v = 10 m/s,
Kinetic energy is given by
1
2
K. E. = × 250 (10)
2
K. E. = 12500 kg m2/ s2
(c) S.I. unit for kinetic energy is joules.
Ans. 16. (a) A ‘Force’ is a vector quantity that can be described as a push or pull on an object
resulting from the object’s interaction with another object. Whenever there is an
interaction between two objects, the objects experience an equal and opposite force on
each other. In other words, both the objects ‘exert force’ on each other. Force only exists
as a result of an interaction. If there is no interaction, the objects no longer experience
the force.
(b)
Mass, m = 1485 kg
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Initial velocity, u = 116 km/hr, in South = –
Final velocity, v = 0
t = 10.25 s
116
m/s
3.6
Fnet = ma
∆v
a =
t
Fnet =
Fnet
m∆v m(v − u)
=
t
t
116 


 0 −
3.6 
= 1485
10.25
Fnet = – 4668.29 kg m/s2
Fnet = – 4.67 × 103 N
Fnet = – 4.67 kN
(c) S.I unit of force is newton (N).
Ans. 17. (a)
→ →
The work done, W = F . s = Fs when a person walk on a horizontal road with load on his
head the q = 90°.
Hence, W = F × s = F × 0 = 0. Thus, no work is done by the person against gravity.
So, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 18. (d)
Let m = mass of the lighter body, V = velocity of the lighter body
M = mass of the heavier body, v = velocity of the heavier body.
Given
mV = Mv
... (i)
1
2
and (KE) of the heavier body = Mv ...(ii)
2
From (i), velocity of the lighter body
V =
Mv
m
...(iii)
1
mV 2 ,
2
Now, replacing the value of V from (iii) in (iv), we get
⇒ KE of lighter body =
...(iv)
2
1  Mv 
M1
1
1
M2 v2
2
 Mv   = m ×
KE of lighter body = mV2 = m 
=
2
m
2
m
2
m
2
2
Now ⇒ M > m, so
M
> 1
m
...(v)
...(vi)
1
1
mV2 > Mv2
2
2
So, KE of lighter body > KE of heavier body
...(vii)
Therefore, the assertion that both the bodies have equal kinetic energy is wrong.
Although the reason is true.
Ans. 19. Work is defined as → a force acting upon an object to → cause a displacement. It is
expressed as the → product of force and displacement in the direction of force. When a
force of 1 newton moves → a body through a distance of 1 metre on its own → direction
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the work done is 1 joule. When both the → force and the displacement are in the same
direction, positive work is done. When force acts in a direction → opposite to the direction
of displacement, the work done is negative.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. The capacity of a body to → do work is called the energy of the body. An object that
possesses energy can → exert a force on another object. When this happens, energy is
transferred from the → former to the latter. The second object may move as it → receives
energy and therefore, does some work. Thus, the first object had the → capacity to do work.
This implies that any → object that possesses energy can do work. The energy possessed by
→ an object is thus measured in terms of its → capacity of doing work.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) Work done is scalar quantity as it has only magnitude and no direction.
(b) Here work done by you is positive work as work is being done in the direction of
displacement unlike in case of gravitational force which acts in downward direction
against the direction of displacement which is in upward direction.
OR
(c) Friction force has done the negative work as its direction is opposite to that of motion.
oo
A-116
Answers Worksheet - 15
Chapter - 4 (Work and Energy)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
Ans. 6.
Ans. 7.
(a) Transferred or converted
(d) Potential energy
(d) Zero
(a) The kinetic energy increases
Kinetic energy.
Electrical energy = Power × Time = 1.2 kw × 10 h = 12 kWh.
The law of conservation of energy states that the total energy of an isolated system remains
constant; it is said to be conserved over time. This law means that energy can neither be
created nor be destroyed; rather, it can only be transformed or transferred from one form
to another.
Ans. 8. Commercial unit of energy : The SI unit joule is too small to express very large quantities
of energy. Hence, we use a bigger unit called kilowatt hour (kWh) to express energy.
1 kWh is the amount of energy consumed by an electrical gadget in one hour at the rate of
1000 J/s or 1 kW.
Ans. 9. Given :
Mass of cart = 10 kg
Distance moved = 20 m
Horizontal force = 60 N
Frictional resistance force = 50 N
...
Net force = 60 – 50 = 10 N
Work done by the horizontal force = 60 × 20 = 1200 J
Work done by the frictional force = – 50 × 20 = – 1000 J
(It is negative because force and displacement are opposite to each other)
Net work done = 1200 J – 1000 J = 200 J
= Change in the K.E. of the cart.
If the cart started from rest, then the initial K.E. = 0
Final K.E. – Initial K.E. = 200 J
So, Final K.E. = 200 J
Ans. 10. Let the mass of each body be m.
For the first body,
Mass = m
Velocity = v
1
So, K.E. of first body = mv2
...(i)
2
For second body,
So, Mass = m
Velocity = 3v
1
K.E. of second body = m (3v)2
2
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=
1
m × 9v2
2
=
9
mv2
2
...(ii)
From (i) and (ii),
1
mv 2
K.E. of first body
1
2
= 9
=
K.E. of second body
9
mv 2
2
Thus, the ratio of the kinetic energies is 1 : 9.
Ans. 11. The initial velocity of an object.
Velocity is the rate that the position of an object changes relative to time. Forces acting on
an object cause it to accelerate. This acceleration changes the velocity. The initial velocity, vi
is the velocity of the object before acceleration causes a change.
Ans. 12. The object which does the work loses energy and the object on which the work is done
gains energy. An object that possesses energy can exert a force on another object. When
this happens, energy is transferred from the former to the latter.
Ans. 13. Given, K.E. = 25J, v = 5 m/s
1
We know,
K.E. = mv2
2
1
25 = m (5)2
2
\
m = 2 kg
(i) If velocity is doubled = 10 m/s, m = 2 kg
1
K.E. =
mv2
2
1
= (2) × (10)2
2
= 100 J
(ii) If velocity is 3 times v = 15 m/s, m = 2 kg
1
K.E. = mv2
2
1
= × 2 (15)2
2
= 225 J.
Ans. 14. (a) When a force F acts on an object to displace it through a distance s in its direction, then
the work done W on the body by the force is given by :
Work done = Force × Displacement
W =F×s
Where,
F = 7 N,
s =8m
Therefore, work done
W =7×8
= 56 Nm
= 56 J
(b) Work is done whenever the given conditions are satisfied :
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(i) A force acts on the body.
(ii) There is a displacement of the body caused by the applied force along the direction
of the applied force.
Ans. 15. (a) Work done by the bullocks is given by the expression
Work done = Force × Displacement
W =F×s
Where,
Applied force, F = 140 N
Displacement, s = 15 m
W = 140 ×15 = 2100 J
Hence, 2100 J of work is done in ploughing the length of the field.
(b) Let us consider an object of mass 'm' which is at rest on smooth horizontal plane.
Let a force, F acts on the object and let the object from rest moves from point A to point
B and covers a displacement s.
The work done by force on the object is :
Workdone = Force × Displacement
W =F×s
...(i)
from third equation of motion :
v2 – u2 = 2as
v 2 − u2
s =
...(ii)
2a
By Newton’s second law of motion :
F = ma
From equations (i) and (ii),
m × a × (v 2 − u2 )
W =
2a
As we have assumed object is at rest
u =0
mv 2
W =
2
The work done appears as kinetic energy of the body.
1
...
K.E. =   mv2.
2
Ans. 16. (a) Power is the rate of doing work or the rate of transfer of energy. If W is the amount of
work done in time t, then power is given by the expression
Energy
Work
Power =
=
Time
Time
P =
W
t
It is expressed in watt (W).
(b) The body is said to have the power of 1 watt if it does work at a rate of 1 joule/sec
1J
i.e.,
1W =
1s
(c) Power is given by the expression,
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Power =
Work done
Time
Work done = energy consumed by the lamp = 1000 J
Time = 10 s
1000
Power =
= 100 Js–1 = 100 W
10
Ans. 17. (c)
Rate of change of momentum is proportional to external forces acting on the system.
The total momentum of the whole system remains constant when no external force is acted
upon it. Internal forces can change the kinetic energy of the system but not the momentum.
Thus, assertion is true but reason is false.
Ans 18. (a)
When the water is at the top of the fall it has potential energy mgh (where m is the mass of
the water and h is the height of the fall).
On falling, this potential energy is converted into kinetic energy is which further converted
into heat energy and so the temperature of water increases.
Thus, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 19. The power is defined as the → time rate of doing work. Power requires both a change in the
→ physical system and a specified time in which the change occurs. This is distinct from
the → concept of work, which is only measured in terms of a → net change in the state of
the physical system. The same amount of → work is done when carrying a load up a flight
of stairs whether the → person carrying it walks or runs, but more power is needed for
running because → the work is done in a shorter amount of time.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. Law of conservation of → energy states that energy can neither be created nor be destroyed,
but it can be → transformed from one form to another. The total energy before and after the
→ transformation remains the same. In an isolated system such as the universe, if there is
a loss of → energy in some part of it, there must be a gain of → an equal amount of energy
in some other part of the universe. Although this principle cannot be proved, there is not
an example of a → violation of the law of conservation of energy.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) At point A, the kinetic energy of the ball is maximum as the height is zero so entire
potential energy is converted into kinetic energy.
(b) At point C the potential energy of the ball is maximum because of its height from the
ground.
(c)
S.No
Kinetic Energy
Potential Energy
Potential Energy is the type of
1.
Kinetic energy is the kind of energy
energy present in a body due to the
present in a body due to the property
property of its state
of its motion
2.
It can be easily transferred from one
It is not transferable
body to another
3.
Kinetic energy can be determined by
Potential energy can be determined
the formula
by the formula
1
P.E. = mgh
K = mv2
2
OR
(d) Kinetic energy exists in moving bodies.Potential energy exists in an object suspended
on a spring.
oo
A-120
Answers Worksheet - 16
Chapter - 5 (Sound)
Ans. 1.
Ans. 2.
Ans. 3.
Ans. 4.
Ans. 5.
(d) Cochlea
(a) An echo
(b) 25 kHz
(c) Longitudinal
The sound waves produced bounce back or get reflected from the mountain or buildings
and come to our ears, this reflected sound is known as Echo. To hear an echo, the barrier
reflecting the sound should be least at a distance of 17 metres.
Ans. 6. Infrasound.
1
Ans. 7.
Frequency (f) =
Time period
=
1
0.025
= 40 Hz
Therefore, the frequency of the wave = 40 Hz.
Ans. 8. Sound is produced by vibrating objects. The matter or substance through which sound
is transmitted is called a medium. It can be solid, liquid or gas. Sound moves through a
medium from the point of generation to the listener.
Ans. 9. When the school bell vibrates, it forces the adjacent particles in the air to vibrate. This
disturbance gives rise to a wave and when the bell moves forward, it pushes the air in front
of it. This creates a region of high pressures known as compression. When the bell moves
backwards, it creates a region of low pressure known as rarefaction. As the bell continues
to move forward and backwards, it produces a series of compressions and rarefactions.
This makes the sound of a bell propagate through air.
Ans. 10. Given,
Time in which echo returned, t = 6 s,
Speed of sound, v = 342 m/s
Distance = Speed × Time = 342 × 6 = 2052 m
As this distance is twice the distance of reflecting surface from the source.
2052
So, the distance of reflecting surface from source =
= 1026 m.
2
Ans. 11. A wave is a disturbance that moves through a medium when the particles of the medium
set neighbouring particles into motion. They, in turn produce similar motion in others. The
particles of the medium do not move forward themselves, but the disturbance is carried
forward.
Ans. 12. Sound waves force the medium particles to vibrate. Hence, these waves are known as
mechanical waves. Sound waves propagate through a medium because of the interaction
of the particles present in that medium.
Ans. 13. (a) The relation between frequency and wavelength of a sound wave is given as follows :
Velocity = Wavelength × Frequency
v =l×n
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This means that the speed is equal to the product of wavelength and frequency of the
sound wave. This equation is also called the ‘wave equation’ and applicable to all types
of wave.
(b) The characteristic of sound involved in uniqueness of the sound is the quality of sound or
timbre.
Sound “quality” or “timbre” describes those characteristics of sound which allow the
ear to distinguish sounds which have the same pitch and loudness. Timbre is then a
general term for the distinguishable characteristics of a tone.
Ans. 14. (a) Time period (T)
It is defined as the time required to complete one cycle of a wave.
A time period (denoted by ‘T’) is the time taken for one complete cycle of
vibration to pass a given point. As the frequency of a wave increases, the time period
of the wave decreases. The unit for the time period is ‘second’.
(b) Speed of sound (v) = Wavelength (λ) × Frequency (ν)
The speed of sound is the distance travelled per unit time by a sound wave as it
propagates through an elastic medium. At 20 °C, the speed of sound in air is about 343
metres per second, or a kilometre in 2.9 s or a mile in 4.7 s.
(c) 0.0195 sec
Here is an example of a problem with a lot of extraneous information.
The period is simply the reciprocal of the frequency.
In this case, the period is
which is 0.0195 second.
1
(51 ⋅ 2Hz)
Ans. 15. (a) Given, Number of vibrations in one minute = 12000
Number of vibrations in one sec =
12000
60
= 200 Hz
Therefore, Frequency of vibration in hertz
ν = 200 Hz
(b) Given, Velocity of sound in air,
v = 360 m/s
Frequency, ν = 200 Hz
v = ν λ
v
or Wavelength of the wave produced l =
ν
360
=
= 1.8 m
200
Ans. 16. (a) Electromagnetic waves can travel in vacuum. Sun light, X-rays are examples of
electromagnetic waves.
In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or
their quanta, photons) of the electromagnetic field, propagating (radiating) through
space, carrying electromagnetic radiant energy. It includes radio waves, microwaves,
infrared, (visible) light, ultraviolet, X-rays, and gamma rays.
(b)
Sound is heard only when the frequency of the wave is greater than 20 Hz. As a simple
pendulum produces waves less than 20 Hz it cannot be heard.
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Human beings can normally hear sounds with a frequency between about 20 Hz and
20,000 Hz. Sounds with frequencies below 20 hertz are called infrasound. Infrasound is
too low-pitched for humans to hear. Sounds with frequencies above 20,000 hertz are
called ultrasound.
(c) Given : Height of the tower, s = 500 m
Velocity of sound,
v = 340 m s–1
Acceleration due to gravity, g = 10 m s–2
Initial velocity of the stone, u = 0
(since the stone is initially at rest)
Time taken by the stone to fall to the base of the tower, t1
According to the second equation of motion :
1 2
s = ut1 + gt1
2
500 = 0 × t1 +
1
× 10 × t12
2
t12 = 100
t1 = 10s
Now, time taken by the sound to reach the top from the base of the lower,
500
t2 =
= 1.47s
340
where,
t = t1 + t2 = 10 + 1.47 = 11.47s.
Ans. 17. (b)
A vacuum refers to space with no air which means there is no medium or no particle present
in it.
The sound is energy which requires a medium to travel from one place to another place.
This energy travels in a vibration form which disturbs particles to move. This disturbance
occurs in with compression and rarefaction processes. When there is no particle in the
space then there is no medium to transfer. So there is no way for the sound to travel.
Thus, both assertion and reason are true but reason is not the correct explanation of
assertion.
Ans. 18. (a)
A sound with higher vibration has a higher frequency which means the compression and
rarefaction are taking place at a faster rate. This means the pitch of the sound is higher. The
pitch differs according to the frequency of the sound.
The sound produced by the mosquito has a lower pitch than the sound produced by the
bee. So, both the sounds are different from each other.
Thus, both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 19. Sound is mechanical energy which → causes a sensation of hearing. As the sound
propagates in the form of → mechanical waves it needs a medium with the → properties
of inertia and momentum. Sound travels through → gases, liquids and solids. The speed
of sound is the → maximum in solids, less in liquids and the least in gases. Sound cannot
travel through → a vacuum because there is no particle to exhibit → the properties of
elasticity and inertia in a vacuum.
[Words marked in BOLD are new information which is not mentioned]
Ans. 20. The human ear can hear the sound between → frequencies of 20 Hz to 20,000 Hz. Thus,
audible range or range of hearing is between → 20 Hz to 20,000 Hz; for human beings.
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However, children under 5 years of age can → hear the sound up to 25000 Hz sound,
below the → frequency of 20 Hz is called infrasonic or infrasound. Infrasound is produced
because of → very slow vibration. For example, simple pendulum produces → sound
below 20 Hz. A human being cannot hear → infrasound as their ears are not adapted to
hear the sound of such range.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) Sound needs a material medium for their propagation like solid, liquid or gas to travel
because the molecules of solid, liquid and gases carry sound waves from one point
to another. Sound cannot progress through the vacuum because the vacuum has no
molecules which can vibrate and carry the sound waves.
(b) As steel is a solid, the speed of sound in steel is 5920 m/s.Water is a liquid so the speed
of sound in water is 1430 m/s and the speed of sound in air is 340 m/s.
(c) Sound travels fastest in solids > Liquids > gases.
OR
(d) This statement is true.When an object is set into vibrations, the sound is produced.
For example, the vibrating diaphragm of a drum produces sound, the vibrating string
of a guitar produces sound, the vibrating diaphragm of speakers of a radio produces
sound, the vibrating end of a drilling machine produces sound, etc.
oo
A-124
Answers Worksheet - 17
Chapter - 5 (Sound)
Ans. 1. (d) 0.1 s
Ans. 2. (c) Vibration of different objects
Ans. 3. (b) Higher energy
Ans. 4. (a) Collects sound waves
Ans. 5. The wave can be characterised by the following parameters:
(i) Frequency
(ii) Amplitude
(iii) Speed
Ans. 6. The frequency of the vibration of a sound produced by a guitar is greater than that produced
by a car horn. Since the pitch of a sound is proportional to its frequency, the guitar has a
higher pitch than a car horn.
Ans. 7. The time taken for one complete oscillation in the density of the medium is called the
time period of the sound wave. It is represented by the symbol T. Its S.I. unit is second (s).
Frequency and time period are related as follows :
ν = 1/T
Ans. 8. The magnitude of the maximum disturbance in the medium on either side of the mean
value is called the amplitude of the wave. It is usually represented by the letter A. The
loudness or softness of a sound is determined basically by its amplitude.
Ans. 9. Speed, wavelength, and frequency of a sound wave are related by the following equation :
Speed (v) = Wavelength (l) × Frequency (ν)
v =l×ν
Ans. 10. Speed of sound, v = 342 ms–1, Echo returns in time, t = 3s
Distance travelled by sound = v × t = 342 × 3 = 1026 m
In the given time interval, sound has to travel a distance that is twice the distance of the
reflecting surface and the source. Hence, the distance of the reflecting surface from the
1026
source is
m = 513 m
2
Ans. 11. The quality or timbre of a sound is that characteristic which enables us to distinguish one
sound from another having the same pitch and loudness. The sound which is more pleasant
is said to be of rich quality. A sound of a single frequency is called a tone.
Ans. 12. Given :
Frequency, ν = 2 kHz = 2000 Hz
Wavelength, λ = 35 cm = 0.35 m
We know that, speed v of the wave = wavelength × frequency
v = λ × ν = 0.35 m × 2000 Hz = 700 m/s
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Ans. 13. (a)The hertz (symbol : Hz) is the derived unit of frequency in the International System of
Units (S.I.) and is defined as one cycle or vibration per second. Hertz are commonly
expressed in multiples : kilohertz (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz
(109 Hz, GHz), terahertz (1012 Hz, THz), petahertz (1015 Hz, PHz), and exahertz (1018
Hz, EHz).
(b) Hippopotamus and whale
Infrasound is the range of sound pitches that is below human hearing bottom limits
(under 20 Hz). Ultrasound is pitches over the human range of hearing. Many animals
can hear infrasound, however, like whales, elephants, rhinos, hippos, giraffes, alligators,
squid/cuttlefish/octopi, and even pigeons an hear infrasonic wave.
Ans. 14. Reverberation is defined as persistence of sound after the source has stopped emitting
sound.
This is due to multiple reflections of sound waves.
Reverberation time is the time required for the sound to “fade away” or decay in a closed
space. Reverberation reduces when the reflections hit surfaces that can absorb sounds such
as curtains, chairs and even people. The reverberation time of a room or space is defined as
the time it takes for sound to decay by 60 dB.
Ans. 15. (a) Time taken to hear the echo, t = 5 s
Distance of the object from the submarine, d = 3625 m
Total distance travelled by the sonar waves during the transmission and reception in
water = 2d
Velocity of sound in water,
v =
2d
2 × 3625
=
= 1450 m s–1
t
5
(b) We know that light travels at a great speed as compared to that of sound, therefore, the
flash of light of ‘lightning’ will reach the man in no time but sound takes 4 seconds to
reach the man.
Now,
and
We know that :
Speed of sound = 330 m/s
Distance = ? (to be calculated)
Time = 4 s
Speed =
Distance
Time
Distance
4
Distance = 330 × 4 m
330 =
= 1320 m
Thus, lighting is at a distance of 1320 metres from the man.
Ans. 16. Sound is a mechanical wave and needs a material medium to propagate. It cannot travel in
vacuum and can be shown by the following experiment.
(i)Take an electric bell and an airtight glass bell jar. The electric bell is suspended inside
the airtight bell jar. Switch ‘ON’ the electric bell.
(ii) Now, connect the bell jar to vacuum pump.
(iii)Pump out the air from the jar, the sound becomes fainter, although the same current
passes through the bell.
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(iv) Pump out some more air from the jar, a very feeble sound is heard.
(v) When the air is completely removed from the jar, no sound is heard.
Ans. 17. (c)
In humidity, air become densor and hence, velocity of sound will be more. Thus, velocity of
sound depends upon the medium.
(A) is true but (R) is false.
Ans. 18. (b)
The sound engineers prefer curved ceilings because the curved surfaces reflect the sound
to all the corners of the room. This helps the audience to hear the sound properly.
The pressure and density of the medium influences the speed of sound. If the pressure and
temperature are higher than the speed of the sound is also higher.
Thus, both assertion and reason are true but reason is not the correct explanation of
assertion.
Ans. 19. Sound wave also gets → reflected as light waves do. Bouncing back of sound wave from
the → surface of solid or liquid is called reflection of sound. Reflection of sound follows →
the Laws of Reflection as light waves do. This means the angle of → the incident wave and
reflected wave to the normal are equal. For the reflection of → sound, a polished or rough
and big obstacle is necessary.
[Words marked in BOLD are new information which are not mentioned]
Ans. 20. (a)
Echo
Reverberation
It is the reflection of a sound wave off It is created by the reflection of sound waves
a surface.
created by the superposition of echoes.
It is clear and distinguishable.
It is less clear comparatively.
(b) No,as we know the minimum distance of the obstacle from the source of sound must
be 17.2 m. So we cannot hear echo in this case.
(c) Speed of sound, v = 346 m/s
Time taken for hearing the echo, t = 1 s
Distance travelled by the sound= v × t = 346 m/s × 1 s = 346 m
In 1 s, sound has to travel twice the distance between the obstacle and the person.
Hence, the distance between the obstacle and the person= 346/2 = 173 m.
OR
(d) A certain amount of reverberation improves the quality of sound of orchestral and
choral music. However, excessive reverberation makes the speech or music indistinct.
oo
A-127
Progress Check - 2
Ans. 1. (c) 100 J
Ans. 2. (a) Power
Ans. 3. (d) All of these
Ans. 4. (c) Temperature of the medium.
Ans. 5. Remains constant.
The total energy of the system is always conserved, so when a body falls freely towards the
earth, then its total energy remains constant i.e., the sum of the potential energy and kinetic
energy of the body would be same at all points.
Ans. 6. The change in the kinetic energy of an object is equal to the net work done on the object.
This fact is referred to as the work-energy principle and is often a very useful tool in solving
mechanics problems.
Ans. 7. Work can be defined as the transfer of energy. In physics, we say that work is done on an
object when we transfer energy to that object. If one object transfers (gives) energy to a
second object then the first object does work on the second object. Work is the application
of a force over a distance.
Ans. 8. Energy is the strength needed to perform work, while the rate at which work is performed
is called power. The unit of measurement of energy and work is termed as joule, whereas,
a watt is the measurement unit of power.
Ans. 9. The wave can be characterised by the following parameters :
(i) Frequency
(ii) Amplitude
(iii) Speed
Ans. 10. When the speed of an object exceeds the speed of sound, it is said to travel in supersonic
speed. For example, bullets, jet crafts etc. travel in supersonic speed.
Ans. 11. The time taken for one complete oscillation in the density of the medium is called the
time period of the sound wave. It is represented by the symbol T. Its S.I. unit is second (s).
Frequency and time period are related as follows :
1
f=
T
Ans. 12. The magnitude of the maximum disturbance in the medium on either side of the mean
value is called the amplitude of the wave. It is usually represented by the letter A. The
loudness or softness of a sound is determined basically by its amplitude.
Ans. 13. (a)Energy can niether be created nor be destroyed, it can only be transformed from one
from to another. Total energy of an isolated system remains same at every points.
Proof : Consider a body of mass 'm' held at rest a height 'h' above the ground.
P.EA = mgh
KEA = 0
(TE)A = PEA + KEA
= mgh + 0
TEA = mgh
...(i)
x
Let the body be dropped from point A so that it falls through a distance 'x'
and is at position-B.
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At position B,
2
PEB = mg (h – x) ⇒ mgh – mgx
vB – uB2 = 2gx
[initially at rest]
vB2 = 2gx
1
1
KEB = mvB2 ⇒ m × 2gx
2
2
KB = mgx
(TE)B = PEB + KEB
= mgh – mgx + mgx
TEB = mgh
When the body is about to touch the ground
At position – C,
2
...(ii)
PEC = 0
vC – uC2 = 2gh
vC2 = 2gh
1
KEC = mvC2
2
KEC =
1
m.2gh = mgh
2
(TE)C = PEC + KEC
= 0 + mgh
(TE)C = mgh
...(iii)
From equation (i), (ii) and (iii), we can conclude that total energy at every point for a freely
falling body remain the same.
(b) Remember to convert the speed into metres per second.
Em = Ek + Ep
1
Em =
mv 2 + mgh
2
Em =
1
(14,300)(59.4)2 +14,300(9.81)(497)
2
Em = 94948425 = 9.50 × 10+7 J
Notice that the calculation and the answer have nothing to do with the direction, since
energy is scalar.
Ans. 14. If there was friction, then it would not be an isolated system.
The frictional force would result in some heat being given off, which would be energy
leaving the system.
At the top of the hill, the person isn’t moving, so Ek will be zero.
At the bottom of the hill the Ep will be zero because the person is zero metres above the
reference point.
Ek + Ep = Ek’ + Ep’
1
1
mv2 + mgh = mv’2 + mgh’
2
2
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0 + (37.3) × (9.81) (23.7) =
1
(37.3) v’2 + 0
2
8672.14 = 18.7 v’2
v’2 = 463.75
= 21.6 m/s
Notice how in this example all of the potential energy the object had at the top of the
hill has been turned completely into kinetic energy at the bottom.
Ans. 15. (a) First of all we will calculate the mass 'm' of the object.
1
Now,
Kinetic energy = mv2
2
So, 25 =
1
× m × (5)2
2
25 =
1
× m × 25
2
m =
25 × 2
25
So, Mass, m = 2 kg
(i)In the first case, the velocity of 5 ms–1 is doubled, so that velocity becomes
5 × 2 = 10 m s–1.
1
Now,
Kinetic energy = mv2
2
=
1
× 2 × (10)2
2
=
1
× 2 × 100
2
= 100 J
(ii) Thus, when the velocity of object is doubled, then its kinetic energy becomes 100 J.
In the second case, the velocity of 5 ms–1 is increased three times so the velocity
becomes 5 × 3 = 15 ms–1.
1
Now,
Kinetic energy =
mv2
2
=
1
× 2 × (15)2
2
=
1
× 2 × 225
2
= 225 J
Thus, when the velocity of object is incresed times, then kinetic energy becomes 225 J.
Ans 16. Sound needs material medium for its propagation from one place to another place. In other
words, sound cannot travel through vacuum. Since there is a region in between the planets
and the earth, where there is a vacuum, so the sound of explosions taking place on other
planets cannot pass through this vacuum. Hence cannot reach the earth.
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Ans. 17. (a)
We know that the weight of an object on the Earth is six times the weight of the object on
the Moon. The weight of an object on the Earth is the force with which the Earth attracts
that object whereas the weight of an object on the Moon is the force with which the Moon
attracts the same object. The attractive force of the Moon is lesser than the attractive force
of the Earth due to the mass of the Moon is lesser than the mass of the Earth.
Thus both assertion and reason are true and reason is the correct explanation of assertion.
Ans. 18. (c)
The sound produced by the lioness and its cub is different because the cub’s sound is softer
as compared to lioness’s sound. The medium does not play any role in the loudness and
softness whereas the amplitude of the sound determines the loudness and softness of the
sound.
Amplitude is the measure of change of the sound per time period.
If the amplitude of the sound is large then the sound is produced for trough or crest of the
wave if higher for a single time period, so, the sound is louder. Therefore, the sound of the
lioness has higher amplitude than it's cub which means the lioness is louder than a cub.
Thus, assertion is true but reason is false.
Ans. 19. (c)
For conservative forces, the sum of kinetic and potential energies at any point remains
constant throughout the motion. This is known as the law of conservation of mechanical
energy.
According to this law,
Kinetic energy + Potential energy = constant or ∆K + ∆U = 0 or ∆K = –∆U.
Thus, the assertion is true but reason is false.
Ans. 20. Ultrasound is sound waves with frequencies → higher than the upper audible limit of
human hearing. Sound, above the → frequency of 20000 Hz is called ultrasound. Humans
cannot hear the ultrasonic sound. Ultrasound is not different from → the “normal” (audible)
sound in its physical properties, except that humans cannot hear it. This limit varies from
person to person and is → approximately 20 kilohertz (20,000 hertz) in healthy young
adults.
[Words marked in BOLD are new information which is not mentioned]
Ans. 21. (a) Buoyancy (also known as the buoyant force) is the force exerted on an object that is
wholly or partly immersed in a fluid.The symbol for the magnitude of buoyancy is B
or FB.
(b) This happens because of density. As we know iron bars is denser than water so they
sink and cork have lower density than water so they float.
(c) Archimedes’ principle, stated as follows: When a body is immersed fully or partially in
a fluid, it experiences an upward force that is equal to the weight of the fluid displaced
by it.
OR
(d) 1. It is used in designing ships and submarines.
2. Lactometers, which are used to determine the purity of a sample of milk and
3. Hydrometers used for determining density of liquids.
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Ans. 22. (a) The potential energy of stored water is converted into Kinetic energy by turbine and
thus produces electricity.
(b) The rate of doing work is called power.
W
t
P =
The SI unit of power is Watt or J/s.
(c) The energy used in households, industries and commercial establishments are usually
expressed in kilowatt hours. For example, electrical energy used during a month is
expressed in terms of ‘units’. Here, 1 ‘unit’ means 1 kilowatt hour.
1 kWh = 1 kW × 1 h
= 1000 W × 3600s
= 3600000 J
OR
(d) We know that P =
W
t
Here t =10 hours
P = 500 W
Energy(W) = ?
500 =
W
10
W = 5000 Watt-hour
W = 5 KWh
oo
A-132