PRE-MEDICAL_PHYSICS
Build Up Your Understanding
EXERCISE-I (Conceptual Question)
(1)
ELASTIC BEHAVIOUR LONGITUDINAL
5.
having radius R. The force needed to break a
STRESS, YOUNG MODULUS
1.
copper wire of radius 2 R will be :
The diameter of a brass rod is 4 mm and
Young’s modulus of brass is 9 × 1010 N/m 2.
The force required to stretch by 0.1% of its
length is :
2.
(1) 360 N
(2) 36 N
(3) 144 × 103 N
(4) 36 × 105 N
6.
A brass rod of length 2 m and cross-sectional
If the elongations of the two rods are equal, then
length of the steel rod (L) is
(YBrass = 1.0 × 1011 N/m2 and
Lw. Then relative density of the material of the
YSteel = 2.0 × 1011 N/m2 )
weight is
Lw
(2) L
a
7.
(1) 1.5 m
(2) 1.8 m
(3) 1 m
(4) 2 m
Two identical rods in geometry but of different
materials having co-efficients of thermal
Lw
(4) L  L
a
w
expansion 1 and 2 and Young’s modulli Y1 and
Y2 respectively are fixed between two rigid
Two wires of equal length and cross-section area
massive walls. The rods are heated such that
suspended as shown in figure. Thier Young's
they undergo the same increase in temperature.
modulus are Y 1 and Y 2 respectively. The
There is no bending of the rods. If 1 : 2 = 2 : 6
equivalent Young's modulus will be
the thermal stresses developed in the two rods
(1) Y1 + Y2
are equal provided Y1 : Y2 is equal to :
Y1  Y2
2
Y1Y2
(3) Y  Y
1
2
(4) F/4
opposite pulls of magnitude 5 × 104 N at its ends.
completely in water, the extension is reduced to
(2)
(3) 4 F
The compound rod is subjected to equal and
expands by La and when the weight is immersed
3.
(2) 2 F
rod of length L and cross-sectional area 1.0 cm2.
support. When loaded with a weight in air, it
La
(3) L
w
(1) F/2
area 2.0 cm2 is attached end to end to a steel
A steel wire is suspended vertically from a rigid
La
(1) L  L
a
w
A force F is needed to break a copper wire
8.
(1) 2 : 3
(2) 1 : 1
(3) 3 : 1
(4) 4 : 9
If the ratio of lengths, radii and Young’s modulii
of steel and brass wires in the figure are a, b, c
respectively. Then the corresponding ratio of
(4)
4.
Y1 Y2
The load versus elongation graph for four wires of
increase in their lengths would be :
(1)
2ac
b2
the same materials is shown in the figure. The
thinnest wire is represented by the line
(2)
3a
2b 2c
(1) OC
(2) OD
(3)
3c
2ab2
(3) OA
(4) OB
Page # 256
(4)
2a 2 c
b
PRE-MEDICAL_PHYSICS
9.
Two wires of the same material and length but
15.
diameter in the ratio 1 : 2 are stretched by the
Two wires of the same material have lengths in
the ratio 1 : 2 and their radii are in the ratio 1 : 2 .
same force. The ratio of potential energy per unit
volume for the two wires when stretched will be :
If they are stretched by applying equal forces, the
(1) 1 : 1
(2) 2 : 1
increase in their lengths will be in the ratio :–
(3) 4 : 1
(4) 16 : 1
(1) 2
(2)
10.
2 :2
W hich one of the following substances
(3) 1 : 1
possesses the highest elasticity :–
(4) 1 : 2
(1) Rubber
(2) Glass
(3) Steel
(4) Copper
16.
The area of cross–section of a wire of length 1.1
meter is 1 mm2. It is loaded with 1 kg. If Young’s
11.
The lower surface of a cube is fixed. On its upper
modulus of copper is 1.1 × 1011 N/m2, then the
surface, force is applied at an angle of 30° from
increase in length will be (If g = 10 m/s2) :–
its surface. The change will be in its :–
(1) 0.01 mm
(1) Shape
(2) 0.075 mm
(2) Size
(3) 0.1 mm
(4) 0.15 mm
(3) Volume
(4) Both shape and size.
17.
The Young’s modulus of a rubber string 8 cm long
and density 1.5 kg/m 3 is 5 × 10 8 N/m 2 , is
12.
A 2m long rod of radius 1 cm which is fixed from
suspended on the ceiling in a room. The increase
one end is given a twist of 0.8 radians. The shear
in length due to its own weight will be :–
strain developed will be :–
(1) 9.6 × 10–5 m
(1) 0.002
(2) 0.004
(2) 9.6 × 10–11 m
(3) 0.008
(4) 0.016
(3) 9.6 × 10–3 m
(4) 9.6 m
13.
If the density of the material increase, the value
of Young’s modulus :–
(1) increases
(2) decreases
18.
One end of uniform wire of length L and of weight
W is attached rigidly to a point in the roof and a
weight W is suspended from its lower end. If s
1
is the area of cross–section of the wire, the stress
(3) first increases, then decreases
(4) first decreases, then increases
14.
The following four wires are made of the same
material. Which of these will have the largest
extension when the same tension is applied–
(1) Length 50 cm and diameter 0.5 mm
(2) Length 100 cm and diameter 1 mm
(3) Length 200 cm and diameter 2 mm
(4) Length 300 cm and diameter 3 mm
in the wire at a height
(1)
L
from its lower end is :–
4
W1
s
W

 W1 + 4 
(2) 
s
3W 

 W1  4 

(3) 
s
(4)
W1 + W
4
Page # 257
PRE-MEDICAL_PHYSICS
19.
A steel wire 1.5 m long and of radius 1 mm is
22.
In determination of young modulus of elasticity
attached with a load 3 kg at one end the other
of wire, a force is applied and extension is
end of the wire is fixed it is whirled in a vertical
recorded. Initial length of wire is '1m'. The curve
circle with a frequency 2Hz. Find the elongation
between extension and stress is depicted then
of the wire when the weight is at the lowest
Young modulus of wire will be:
11
position– (Y = 2 × 10 N/m² and g = 10 m/s²)
20.
(1) 1.77 × 10–3 m
(2) 7.17 × 10–3 m
(3) 3.17 × 10–7 m
(4) 1.37 × 10–7 m
A copper wire of length 3m and area of cross–section 1 mm2, passes through an arrangement of
two frictionless pulleys, P1 and P2. One end of
the wire is rigidly clamped and a mass of 1 kg
is hanged from the other end. If the Young's
modulus for copper is 10 × 1010 N/m2, then the
(1) 2 × 109 N/m2
(2) 1 × 109 N/m 2
elongation in the wire is–
(3) 2 × 1010 N/m 2
(4) 1 × 1010 N/m 2
23.
1m
P1
A block of mass 'M' area of cross–section 'A' &
length '' is placed on smooth horizontal floor. A
force 'F' is applied on the block as shown. If Y
1m
P2
is young modulus of material , then total
extension in the block will be:
1m
Area 'A'
F
21.
(1) 0.05 mm
(2) 0.1 mm
(3) 0.2 mm
(4) 0.3 mm

(1)
Fl
AY
(2)
Fl
2AY
(3)
Fl
3AY
(4) cannot extend
One end of a long metallic wire of length L area
of cross section A and Young's modulus Y is tied
to the ceiling. The other end is tied to a massless spring of force constant k. A mass m hangs
freely from the free end of the spring. It is slightly
pulled down and released. Its time period is given
by–
(1) 2
m
k
(2) 2 
mYA
kL
24.
The maximum stress that can be applied to the
material of a wire used to suspend an elevator is
3
× 108 N/m2. If the mass of elevator is 900 kg

and it move up with an acceleration 2.2 m/s2 then
calculate the minimum radius of the wire..
(1) 6 mm
(3)
(4)
4mm
(2) 7 mm
(3) 8 mm
(4) 5 mm
Page # 258
PRE-MEDICAL_PHYSICS
25.
Two wires of diameter 0.25 cm, one made of steel
28.
A catapult's string made of rubber having cross
section area 25 mm 2 and length 10 cm. To
and other made of brass are loaded as shown
throw a 5 gm pebble it is stretched up to 5 cm
and released. Velocity of projected pabble is
in figure. The unloaded length of steel wire is 1.5
(Young coefficient of elasticity of rubber is
m and that of brass wire is 1.0 m. Young's
5 × 108 N/m 2) :
modulus of steel is 2.0 × 1011 Pa and that of
(1) 20 m/s
(2) 100 m/s
(3) 250 m/s
(4) 200 m/s
brass is 0.91 × 1011 Pa. Calculate the elongation
29.
of steel and brass wires. (1 Pa = 1 Nm–2)
Diameter of a brass rod is 4 mm and Young
coefficient of elasticity is 9 × 1010 N/m 2. Force
required to increase the length of rod by 0.10%
will be :
(1) 360  N
(3) 144×
(2)
103
(2) 36 N
N
(4) 36 × 105 N
TANGENTIAL STRESS AND STRAIN, SHEAR
MODULUS
30.
A square brass plate of side 1.0 m and thickness
0.005 m is subjected to a force F on its smaller
(1) Steel wire : 1.49 × 10–4 m, Brass wire :
opposite edges, causing a displacement of 0.02 cm.
1.31 × 10–4 m
If the shear modulus of brass is 0.4 × 1011 N/m2,
(2) Steel wire : 1.60 × 10–3 m, Brass wire :
the value of the force F is
1.31 × 10–5 m
(1) 4 × 103 N
(3) Steel wire : 1.30 × 10–5 m, Brass wire :
4
(3) 4 × 10 N
(2) 400 N
(4) 1000 N
1.31 × 10–5 m
(4) Steel wire : 1.22 × 10–2 m, Brass wire :
31.
1.44 × 10–4 m
The upper end of a wire of radius 4 mm and length
100 cm is clamped and its other end is twisted
through an angle of 30°. Then angle of shear is
26.
The breaking stress of a wire depends upon
(1) Length of the wire
(1) 12°
(2) 0.12°
(3) 1.2 °
(4) 0.012°
(2) Radius of the wire
32.
(3) Material of the wire
A 2m long rod of radius 1 cm which is fixed from
one end is given a twist of 0.8 radians. The shear
(4) Shape of the cross section
strain developed will be
27.
1010
N/m 2)
of
(1) 0.002
(2) 0.004
diameter 3 mm supports a 40 kg mass. In order
(3) 0.008
(4) 0.016
A 5m aluminium wire (Y = 7 ×
to have the same elongation in a copper wire
(Y= 12 × 1010 N/m 2) of the same length under
the same weight, the diameter should be in
mm
(1) 1.75
(2) 2.0
(3) 2.3
(4) 5.0
33.
A 50 kg motor rests on four cylindrical rubber
blocks. Each block has a height of 4 cm and a
cross-sectional area of 16 cm 2. The shear
modulus of rubber is 2 × 106 N/m2. A sideways
force of 500 N is applied to the motor. The
distance that the motor moves sideways is
(1) 0.156 cm
(2) 1.56 cm
(3) 0.312 cm
(4) 0.204 cm
Page # 259
PRE-MEDICAL_PHYSICS
(3)
PRESSURE AND VOLUMETRIC STRAIN, BULK
40.
'Mg' weight and the increase in length is '  '
MODULUS OF ELASTICITY
34.
Calculate the work done, if a wire is loaded by
A metal block is experiencing an atmospheric
pressure of 1 × 105 N/m2, when the same block
(1) Mg 
(2) Zero
(3) Mg  /2
(4) 2Mg 
is placed in a vacuum chamber, the fractional
change in its volume is (the bulk modulus of metal
41.
per unit volume is
is 1.25 × 1011 N/m2)
(1) 4 × 10–7
(2) 2 × 10–7
–7
–7
(3) 8 × 10
35.
(3)
36.
(4) 1 × 10
The relation between ,  and K for a elastic
material is
1
1
1

(1) 
 3  9K
1
1
1


 3K 9
(4)
(3) 2
(2)
(4) FL/2
A wire of length 50 cm and cross sectional area
(3) 2  10–2 J
(4) 1  10–2 J
43.
When a force is applied on a wire of uniform crosssectional area 3 × 10–6 m2 and length 4m, the
increase in length is 1 mm. Energy stored in it
will be (Y = 2 × 1011 N / m2)
(4) 
(1) 6250 J
(2) 0.177 J
(3) 0.075 J
(4) 0.150 J
An increase in pressure required to decrease the
container is : (Bulk modulus of the liquid = 2100
44.
(1) 188 kPa
(3) 18.8 kPa
The elastic energy stored in a wire of Young's
modulus Y is
MPa) :–
38.
(3) FL/2A
(2) 4  10–2 J
1

200 litres volume of a liquid by 0.004% in
(4)
(2) FA/2L
work will be (Y = 2  1010 Nm–2)
(1) 6  10–2 J
1
1
1


 3 9K
constant force F is proportional to :–
1
2
(1) F  /2AL
of 1 sq. mm is extended by 1 mm. The required
1
1
1


(2)
K 3  9
 . The extension produced in this wire by a
37.
42.
A fixed volume of iron is drawn into a wire of length
(1)
On stretching a wire, the elastic energy stored
(2) 8.4 kPa
(1) Y ×
(4) 84 kPa
Strain 2
Volume
(2) Stress × Strain × Volume
ELASTIC POTENTIAL ENERGY
If the potential energy of a spring is V on
(3)
Stress 2  Volume
2Y
(4)
1
Y × stress × Strain × Volume
2
stretching it by 2 cm, then its potential energy
when it is stretched by 10 cm will be :
(1) V/25
(2) 5 V
(3) V/5
(4) 25 V
45.
39.
A wire of length 50 cm and cross sectional area
If work done in stretching a wire by 1mm is 2J,
of 1 sq. mm is extended by 1 mm. The required
the work necessary for stretching another wire of
work will be (Y = 2 × 1010 Nm–2)
same material, but with double the radius and
(1) 6 × 10–2 J
half the length by 1mm in joule is (1) 1/4
(2) 4
(3) 8
(4) 16
Page # 260
(2) 4 × 10–2 J
(3) 2 × 10–2 J
(4) 1 × 10–2 J
PRE-MEDICAL_PHYSICS
46.
Two wires of same diameter of the same material
52.
The terminal velocity of a sphere moving
having the length  and 2. If the force F is applied
through a viscous medium is :
on each, the ratio of the work done in the two wires
(1) directly proportional to the radius of the
will be :–
47.
sphere
(1) 1 : 2
(2) 1 : 4
(3) 2 : 1
(4) 1 : 1
(2) inversely proportional to the radius of the
sphere
(3) directly proportional to the square of the
A brass rod of cross–sectional area 1 cm2 and
radius of sphere
length 0.2 m is compressed lengthwise by a
(4) inversely proportional to the square of the
weight of 5 kg. If Young’s modulus of elasticity
radius of sphere
of brass is 1 × 1011 N/m2 and g = 10 m/sec2, then
increase in the energy of the rod will be :–
53.
(1) 10–5 joule
A sphere is dropped gently into a viscous medium
(2) 2.5 × 10–5 joule
of infinite extent. As the sphere falls, the net force
(3) 5 × 10–5 joule
acting downwards on it
(4) 2.5 × 10–4 joule
(1) remains constant throughout
(2) increases for sometime and then becomes
48.
A weight is suspended from a long metal wire. If
constant
the wire suddenly breaks, its temperature :–
(3) decreases for sometime and then becomes
(1) Rises
zero
(2) Falls
(4) increases for sometime and then decreases.
(3) Remains unchanged
(4) Attains a value 0 K
49.
54.
A solid sphere falls with a terminal velocity of
10 m/s in air. If it is allowed to fall in vacuum,
A liquid has only
(1) shear modulus
(2) Young’s modulus
(3) bulk modulus
(4) All of the above
(1) terminal velocity will be more than 10 m/s
(2) terminal velocity will be less than 10 m/s
(3) terminal velocity will be 10 m/s
(4) there will be no terminal velocity
VISCOSITY
50.
51.
An oil drop falls through air with a terminal
55.
If a rubber ball is taken at the depth of 200 m
velocity of 5 × 10–4 m/s.
in a pool its volume decreases by 0.1%. If the
(i) the radius of the drop will be :
density of the water is 1 × 10 3 kg/m 3 and
(1) 2.5 × 10–6 m
(2) 2 × 10–6 m
g = 10 m/s2, then the volume elasticity in N/m 2
(3) 3 × 10–6 m
(4) 4 × 10–6 m
will be :
For previous question the terminal velocity of
(1) 108
(2) 2 × 108
(3) 109
(4) 2 × 109
a drop of half of this radius will be :
56.
18  10 5
(Viscosity of air =
N-s/m 2.
5
liquid. The value of its terminal velocity is proportional
Density of oil = 900 Kg/m 3. Neglect density of
air as compared to that of oil)
–4
(1) 3.25 × 10 m/s
–4
(3) 1.5 × 10 m/s
A ball of mass m and radius r is released in a viscous
–4
(2) 2.10 × 10 m/s
to :
(1)
(4) 1.25 × 10–4 m/s
(3)
1
r
(2)
m
r
m
r
(4) m only
Page # 261
PRE-MEDICAL_PHYSICS
57.
The compressibility of water is 46.4 × 10–6/atm.
60.
This means that
In Poiseuilli's method of determination of
coefficient of viscosity. the physical quantity that
(1) the bulk modulus of water is 46.4 ×
106
atm
requires greater accuracy in measurement is
(2) volume of water decreases by 46.4
(1) Pressure difference
one-millionths of the original volume for each
(2) Volume of the liquid collected
atmosphere increase in pressure
(3) Length of the capillary tube
(3) when water is subjected to an additional
(4) Inner radius of the capillary tube
pressure of one atmosphere, its volume
decreases by 46.4%
61.
(4) When water is subjected to an additional
A viscous fluid is flowing through a cylindrical tube.
The velocity distribution of the fluid is best
pressure of one atmosphere, its volume is
represented by the diagram
reduced to 10–6 of its original volume.
58.
A spherical ball is dropped in a long column of
(1)
viscous liquid. Which of the following graphs
represent the variation of
(2)
F
P
Q
(3)
R
t
O
(4) None of these
(i) gravitational force with time
62.
(ii) viscous force with time
More viscous oil is used in summer than in winter
in motors due to :–
(iii) net force acting on the ball with time.
(1) Rise in temperature in summer, the viscosity
(1) Q, R, P
of oil decreases
(2) R, Q, P
(2) Rise in temperature in summer, viscosity of
(3) P, Q, R
oil increases
(4) P, R, Q
(3) Surface tension of oil increases
(4) Surface tension of oil decreases
59.
A small steel ball falls through a syrup at constant
speed of 10 cm/s. If the steel ball is pulled
upwards with a force equal to twice its effective
weight, how fast will it move upwards ?
(1) 10 cm/s
(2) 20 cm/s
(3) 5 cm/s
(4) – 5 cm/s
Page # 262
63.
With increase in temperature, the viscosity of :–
(1) Gases decreases and liquid increases
(2) Gases increases and liquid decreases
(3) Both gases and liquid increases
(4) Both gases and liquid decreases
PRE-MEDICAL_PHYSICS
64.
A rain drop of radius 0.3 mm has a terminal
67.
velocity in air 1m/s. The viscosity of air is 18 ×
in an experiment to determine the viscosity of the
–5
10 poise. The viscous force on it is :–
liquid, increases :–
(1) 101.73 × 10–4 dyne
(1) When the pressure of the tube is increased
(2) 101.73 × 10–5 dyne
(2) When the length of the tube is increased
–5
(3) When the radius of the tube is decreased
–4
(4) None of the above
(3) 16.95 × 10 dyne
(4) 16.95 × 10 dyne
65.
The rate of flow of liquid through a capillary tube,
Two liquids of densities d1 and d2 are flowing in
68.
A copper ball of radius 'r' travels with a uniform
identical capillaries under same pressure
speed 'v' in a viscous fluid. If the ball is changed
difference. If t1 and t2 are the time taken for the
with another ball of radius '2r', then new uniform
flow of equal quantities of liquids, then the ratio
speed will be :–
of coefficients of viscosities of liquids must be :–
(1) v
(2) 2v
(3) 4v
(4) 8v
d1d 2
(1) t t
1 2
d1t1
(2) d t
2 2
69.
Two drops of equal radius are falling through air
with a steady velocity of 5cm/sec. If the two drops
d1t 2
(3) d t
2 1
(4)
 d1t1 
 d t 
coalesce, then its terminal velocity will be :–
2 2
1
(1) 4 3 × 5 cm / s
66.
The velocity of falling rain drops attain, limited
1
(2) 4 3 cm/s
value because of :–
(1) Surface tension
1
(3) 5 3 × 4 cm / s
(2) Upthrust due to air
(3) Viscous force exerted by air
2
(4) Air current
(4) 4 3 × 5 cm / s
AN SWER -K EY [EXER C ISE- I ]
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Page # 263