PART TEST-1
DATE:13-02-2021
NEET-2021
MOTION IN A PLANE
1. A projectile starts with speed u at an angle θ from 5. A particle of mass 6 kg moves with an initial velocity of
the horizontal ground. The average velocity of the →
ˆ
ˆ
v
= (8 i + 8 j)
m/s. A constant force of
projectile between the point of projection and the point of
→
arrival on the ground is:
ˆ
F = − 30 j N is applied to the particle. Initially, the
particle was at (0, 0). The x-coordinate of the particle,
(1) usinθ
when its y-coordinate again becomes zero is given by
(2) 2usinθ
(1) 6.0 m
(3) ucosθ
(2) 12.8 m
(4) 2ucosθ
(3) 8 m
(4) 25.6 m
2. The trajectory of a projectile in the vertical plane is y = 6. A projectile is projected with speed u at an angle of 30°
ax - bx where a and b are constants, x and y are with the vertical from the ground. The angle between the
horizontal and vertical displacements from point of acceleration of the projectile and its velocity at the time
projection. The angle of projection from the horizontal is
of striking the horizontal ground is:
2
1.
tan
2.
tan
3.
tan
4.
tan
−1
(
a
b
(1) 30°
)
(2) 60°
−1
(b)
(3) 45°
−1
(
−1
b
a
)
(4) 0°
(a)
7. A missile is fired for maximum range with an
initial velocity of 20 m/s, then the maximum height of
3. A particle is thrown horizontally from a pole of height missile is
500 m with an initial speed of 50 m/s. The distance
between the foot of the pole and striking point of the (1) 20 m
particle on the ground is: (g = 10 m/s )
(2) 30 m
(1) 100 m
(3) 10 m
(2) 250 m
(4) 40 m
(3) 500 m
2
(4) 1000 m
8. Two projectiles projected with the same speed at angles θ
and (90° - θ) from the same point, then H × H is
equal to (where symbols have their usual meanings)
1
4. Two balls are projected to acquire same range with
the same initial speed u but at different angles of
projection. If maximum height acquired by balls are
H
and H , then (H
+ H ) is: (angle of projection of
one projectile is θ)
1
2
(1) tan
(2) cot
(3)
u
2
2
2
2g
θ
θ
1
2
1.
R
2.
R
2
2
3.
16
4.
2
R
2
8
9. A particle is moving eastwards with velocity of 5 m/s. In
10 seconds the velocity changes to 5 m/s northwards. The
average acceleration in this time is1. Zero
2.
(4) tan θ
3.
4.
1
m/s
2
√2
1
m/s
√2
1
2
m/s
2
2
toward north-west
toward north-east
toward north-west
Page: 1
2. 50 J
10. If horizontal range of a projectile is 4√3 times its
maximum height. Its range of projection will be
3. 75 J
4. 0 J
1. 45°
2. 60°
14. The equation of trajectory of a projectile given angular
projection is y = ax - bx2, then horizontal range of
projectile is
3. 90°
4. 30°
1.
11. A stone is pfojected with a velocity v at an angle θ with
the horizontal reaches maximum height H1. When it is
2.
with the horizontal,
3.
it reaches maximum height H2. The ratio between
hrizontal range R of the projection, H1 and H2 is ?
4.
projected with u at an angle (
1. R
=
2√ H 1 H 2
2. R
=
√ H1 H2
3. R
=
4√ H 1 H 2
4. R
=
π
2
− θ)
a
b
a
2b
2a
b
a
4b
15. A large number of bullets are fired in all directions with
same velocity u. What is the maximum area on the
ground on which these bullets can spread ?
πu
2.
πu
3.
π u
4.
π u
8√ H 1 H 2
12. The velocity of a projectile at the initial point A is
ˆ
ˆ
(4 i + 5 j) m/s. Its velocity in m/s at point B is
2
1.
g
g
4
2
2
g
2
g
4
2
2
2
16. A particle is thown with a speed u at an angle θ with the
horizontal. When the particle makes an angle ϕ with the
horizontal, its speed changes to v, Which is equal to
1. (4ˆi + 5ˆj)
4. (4ˆi − 5ˆj)
cos θ
2. u
cos θ cos ϕ
3. u
cos θ sec ϕ
4. u sec θ
2. (−4ˆi − 5ˆj)
3. (−4ˆi + 5ˆj)
1. u
cos ϕ
17. A smooth square platform ABCD is moving towards
right with uniform speed u. At what angle θ must a
particle be projected from A with speed v, so that it
strikes the point D ?
13. A body is projected with initial kinetic energy of 100 J
and at an angle of 60° with the horizontal. The K.E. of
the body at highest point will be
1. 25 J
Page: 2
1. sin
−1
2. cos
3. sin
−1
−1
4. cos
(
(
(
−1
(
18.
u
v
v
u
v
u
u
v
)
)
)
)
1. 45
0
2. 60
0
3. 30
0
4. None
20. The height y and the distance x along the horizontal
plane of a projectile on a certain planet (with no
surrounding atmosphere) are given by y = 8t − 5t m
and x = 6t m, where t is in seconds. The velocity with
Time taken by the projectile to reach from P to Q is t,
which
the particle is projected is.
then PQ ?
2
1. 2ut
1. 14 m/s
2. √3 ut
2. 10 m/s
3.
√3
4.
ut
2
3. 8 m/s
ut
4. 6 m/s
√3
21. A particle of mass m is projectile with a velocity v
19. A aeroplane moving with a speed of 250m/s is at a height making an angle of 30 with the horizontal. The
of 6000 m just overhead of an ant, aircraft gun. Muzzle magnitude of angular momentum of the projectile about
the point of the projection when particle is at it's
speed of shell is 500m/s, the firing angle θ should be ?
maximum height h is
o
1. √
3
mv
2
g
2
2. zero
3.
mv
3
√2g
√3
4.
16
mv
3
g
22. if a person can through a stone to maximum height of h
meter vertically, then maximum distance
Page: 3
through which it can be thrown horizontally by the same
person is
1. h/2
3. 1440 m
4. 960 m
27.
2. h
A cart is moving horizontally along a straight line with
contant speed of 30 m/s. A projectile is to be fired from
the moving cart in such a way that it will return to the
cart after the cart has moved 80 m. At what speed
(relative to the cart) must the projectile be fired ? (given
g = 10 m/s2)
3. 2h
4. 3h
23.
At the top of the trajectory of a projectile, direction of its
velocity and acceleration are
1. perpendicular to each other
1. 10 m/s
2.
40
3
m/s
3. 10√8 m/s
2. parallel to each other
4. None of the above
3. inclined to each other at angle of 45
0
28.
4. antiparallel to each other
24.
At the height 80 m an aeroplane is moving with 150m/s.
A bomb is dropped from it, so as to hit a target. At what
distance from the target should bomb be dropped ?
A cart is moving with speed of 20m/s on a horizontal
track. A body is projected with speed 40m/s (relative to
cart ) from the cart in such a way that path of body
appear to be straight line for an observer on ground. Time
for which body remains in air is:
1. 2√3 sec
1. 605.3 m
2. 4 sec
2. 600 m
3. 4√3 sec
3. 80 m
4. 8 sec
4. 230 m
25.
29.
Three balls are dropped from the top of a building with A body is projected with speed u at an angle θ with the
equal speed at different angles. When the balls horizontal after what time it will start moving
perpendicular to its initial direction of projection.
strike ground, their velocities are v , v & v
respectively , than
1. t =
1
2
3
u
g sin 2θ
1. v1 > v2 > v3
2. v3
> v2 >
3. v1
=
4. v1
< v2
v2 =
v1
v3
2. t
=
3. t
=
4. t
=
< v3
26.
An object of mass 2m is projected with a speed of 100
m/s at an angle θ
=
sin
−1
(
3
5
)
to the horizontal. At the
2u
g sin θ
u
2g sin θ
u
g sin θ
30.
Galileo writes that for angles of projection of
highest point, the object breaks into pieces of same mass
m & the first one comes to rest . The distance between
point of landing of the bigger piece is (given g = 10 m/s2
)
1. 3840 m
2. 1280 m
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31.
A particle is projected at an angle θ with horizontal with
an initital speed u. When it makes an angle α with
horizontal, its speed v is1. u cos θ
3.
4.
u cos θ
1. u cos θ
2. u tan θ
2. u cos θ u cos α
u sin θ
A particle is projected with a velocity u making an angle
θ with the horizontal. At any instant, its velocity v is at
right angles to its initial velocity u; then v is:
3. u cot θ
4. u sec θ
sin α
36.
cos α
A projectile is given an initial velocity of ˆi + 2ˆj . The
cartesian equation of its path is (g = 10 ms )
−2
32.
A body is projected with velocity 20√3 m/s with an
angle of projection 60° with horizontal. Calculate
velocity on that point where body makes an angle 30°
with the horizontal.
20
2. y = x − 5x
2
2
3. 4y = 2x − 5x
4. y = 2x − 25x
1. 20 m/s
2.
1. y = 2x − 5x
2
2
37.
m/s
√3
A ship A is moving westwards with a speed of 10 km
h
and a ship B, 100 km south of A is moving
northwards with a speed of 10 km h . The time after
which the distance between them becomes the shortest,
is:
3. 10√3 m/s
−1
−1
4. 10 m/s
33.
A particle is moving with veocity
⇀
ˆ
ˆ
V = k(y i + x j)
;
1. 5 hr
where k is constant. The general equation for path is:
2. 5√2 hr
1. y = x
3. 10√2 hr
2. y
2
2
= x
+ constant
2
+ constant
3. y = x + constant
4. xy=constant
4. 0 hr
38.
Time taken by the projectile to reach from A to B is t.
Then the distance AB is equal to :
34.
A body thrown vertically so as to reach its maximum
height in t second. The total time from the time of
projection to reach a point at half of its maximum height
while returning (in second) is:
1. √2t
2. (1 +
3.
3t
4.
t
2
√2
1.
1
√2
ut
√3
)t
2.
√3ut
2
3. √3ut
4. 2ut
35.
Page: 5
39.
horizontal. Which of the following statements is correct .
The height y and the distance x along the horizontal
plane of a projectile on a certain planet (with no
surrounding atmosphere) are given by y = 8t − 5t m
and x = 6t m, where t is in seconds. The velocity with
which the particle is projected is.
2
3. Range of A and C are equal & greater than that of B
44.
2. 10 m/s
At the height 80 m an aeroplane is moving with 150m/s.
A bomb is dropped from it, so as to hit a target. At what
distance from the target should bomb be dropped ?
3. 8 m/s
4. 6 m/s
40.
1. 605.3 m
A particle of mass m is projectile with a velocity v
making an angle of 30 with the horizontal. The
magnitude of angular momentum of the projectile about
the point of the projection when particle is at it's
maximum height h is
o
1. √
3
mv
2
mv
3. 80 m
4. 230 m
45.
Three balls are dropped from the top of a building with
equal speed at different angles. When the balls
strike ground, their velocities are v , v & v
respectively , than
g
3
1
√2g
√3
2. 600 m
2
2. zero
4.
2. Range of A and C are less than that of B
4. A, B and C have equal ranges
1. 14 m/s
3.
1. A, B and C have unequal ranges
mv
3
3
1. v1 > v2 > v3
g
16
2
41.
2. v3
> v2 >
3. v1
=
v2 =
v1
v3
if a person can through a stone to maximum height of h 4. v < v < v
meter vertically, then maximum distance through which
46.
it can be thrown horizontally by the same person is
An object of mass 2m is projected with a speed of 100
1. h/2
m/s at an angle θ = sin ( ) to the horizontal. At the
2. h
highest point, the object breaks into pieces of same mass
3. 2h
m & the first one comes to rest . The distance between
point of landing of the bigger piece is (given g = 10 m/s2
4. 3h
)
1
2
3
−1
3
5
1. 3840 m
42.
At the top of the trajectory of a projectile, direction of its
velocity and acceleration are
3. 1440 m
4. 960 m
1. perpendicular to each other
2. parallel to each other
3. inclined to each other at angle of 45
2. 1280 m
*******
0
4. antiparallel to each other
43.
These particles A, B and C are projected from the same
pair with same initial speed making angles
30
45 & 60 respectively with the
o,
o
o
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