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# Elasticity JEE Main - Physics, Solution by DC Pandey NEET Notes | EduRev

## DC Pandey (Questions & Solutions) of Physics: NEET

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## NEET : Elasticity JEE Main - Physics, Solution by DC Pandey NEET Notes | EduRev

``` Page 1

EXERCISES
For JEE Main
Subjective Questions
Q 1.  A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400
N is applied to each end of the wire. What minimum diameter is required for the wire ?
Ysteel =2.1 × 10
11
N/m
2

Q 2.  The elastic limit of a steel cable is 3.0 × 10
8
N/m
2
and the cross-section area is 4 cm
2
. Find the
maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the
stress is not to exceed one-third of the elastic limit.
Q 3.  If the elastic limit of copper is 1.5 x 10
8
N/m
2
, determine the minimum diameter a copper wire can
have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Q 4.  Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own
weight. Density of steel = 8000 kg/m
3
and Young's modulus of steel = 2 x 10
11
N/m
2
. What is the
energy stored in the wire ? (Take g = 9.8m/s
2
)
Q 5.  Two wires shown in figure are made of the same material which has a breaking stress of 8 × 10
8

N/m
2
. The area of cross-section of the upper wire is 0.006 cm
2
and that of the lower wire is 0.003
cm . The mass m 1 = 10 kg, m 2 = 20 kg and the hanger is light. Find the maximum load that can be
put on the hanger without breaking a wire. Which wire will break first if the load is increased ?
(Take g = 10 m/s
2
)

Q 6.  A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end
and the combination is subjected to a tension. Find the ratio of:

(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 10
11
N/m
2
and T of copper = 1.3 × 10
11
N/m
2
)
Q 7.  Calculate the approximate change in density of water in a lake at a depth of 400 m below the
surface. The density of water at the surface is 1030 kg/m
3
and bulk modulus of water is 2 ×
10
9
N/m
2
.
Q 8.  A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 10
10
N/m
2
is suspended from a
point and supports a heavy cylinder of volume 10
-3
m
3
at its lower end. Find the decrease in length
when the metal cylinder is immersed in a liquid of density 800 kg/m
3
.
Q 9.  In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction
in the volume of the ball is 0.1%. The density of water of the lake is 1 × 10
3
kg/m . Determine the
value of the bulk modulus of elasticity of rubber. (g = 9.8m/s
2
)
Page 2

EXERCISES
For JEE Main
Subjective Questions
Q 1.  A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400
N is applied to each end of the wire. What minimum diameter is required for the wire ?
Ysteel =2.1 × 10
11
N/m
2

Q 2.  The elastic limit of a steel cable is 3.0 × 10
8
N/m
2
and the cross-section area is 4 cm
2
. Find the
maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the
stress is not to exceed one-third of the elastic limit.
Q 3.  If the elastic limit of copper is 1.5 x 10
8
N/m
2
, determine the minimum diameter a copper wire can
have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Q 4.  Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own
weight. Density of steel = 8000 kg/m
3
and Young's modulus of steel = 2 x 10
11
N/m
2
. What is the
energy stored in the wire ? (Take g = 9.8m/s
2
)
Q 5.  Two wires shown in figure are made of the same material which has a breaking stress of 8 × 10
8

N/m
2
. The area of cross-section of the upper wire is 0.006 cm
2
and that of the lower wire is 0.003
cm . The mass m 1 = 10 kg, m 2 = 20 kg and the hanger is light. Find the maximum load that can be
put on the hanger without breaking a wire. Which wire will break first if the load is increased ?
(Take g = 10 m/s
2
)

Q 6.  A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end
and the combination is subjected to a tension. Find the ratio of:

(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 10
11
N/m
2
and T of copper = 1.3 × 10
11
N/m
2
)
Q 7.  Calculate the approximate change in density of water in a lake at a depth of 400 m below the
surface. The density of water at the surface is 1030 kg/m
3
and bulk modulus of water is 2 ×
10
9
N/m
2
.
Q 8.  A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 10
10
N/m
2
is suspended from a
point and supports a heavy cylinder of volume 10
-3
m
3
at its lower end. Find the decrease in length
when the metal cylinder is immersed in a liquid of density 800 kg/m
3
.
Q 9.  In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction
in the volume of the ball is 0.1%. The density of water of the lake is 1 × 10
3
kg/m . Determine the
value of the bulk modulus of elasticity of rubber. (g = 9.8m/s
2
)
Q 10.  A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m
and diameter 4 mm which is suspended from the ceiling of a room. The point of support is 521 cm
above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes
the floor. Calculate the velocity of the ball at its lowest position. (Y steel =2 × 10
11
N/m
2
)
axis with a frequency v. If density of the wire is p and Young's modulus is Y. Find the fractional
change in radius of the ring.
Q 12.  A 6 kg weight is fastened to the end of a steel wire of unstretched length 60 cm. It is whirled in a
vertical circle and has an angular velocity of 2 rev's at the bottom of the circle. The area of cross-
section of the wire is 0.05 cm
2
. Calculate the elongation of the wire when the weight is at the
lowest point of the path. Young's modulus of steel =2 × 10
11
N/m
2
.
Q 13.  A homogeneous block with a mass m hangs on three vertical wires of equal length arranged
symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of
copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be
double than that of copper.

Q 14.  A uniform copper bar of density length L, cross-sectional area S and Young's modulus Y is
moving horizontally on a frictionless surface with constant acceleration a0. Find :
(a) the stress at the centre of the wire, (b) total elongation of the wire.
Q 15.  A 5 m long cylindrical steel wire with radius 2 × 10
-3
m is suspended vertically from a rigid
support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the
change in temperature of the wire ignoring radiation losses. (Take g =10m/s
2
)
(For the steel wire : Young's modulus =2.1 × 10
11
N/m
2
; Density = 7860 kg/m
3
; Specific heat =
420.T/kg-°C).
Solutions
1.

= 1.9 × 10
-3
m = 1.9 mm
2.  × 3 × 10
8
N/m
2

Page 3

EXERCISES
For JEE Main
Subjective Questions
Q 1.  A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400
N is applied to each end of the wire. What minimum diameter is required for the wire ?
Ysteel =2.1 × 10
11
N/m
2

Q 2.  The elastic limit of a steel cable is 3.0 × 10
8
N/m
2
and the cross-section area is 4 cm
2
. Find the
maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the
stress is not to exceed one-third of the elastic limit.
Q 3.  If the elastic limit of copper is 1.5 x 10
8
N/m
2
, determine the minimum diameter a copper wire can
have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Q 4.  Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own
weight. Density of steel = 8000 kg/m
3
and Young's modulus of steel = 2 x 10
11
N/m
2
. What is the
energy stored in the wire ? (Take g = 9.8m/s
2
)
Q 5.  Two wires shown in figure are made of the same material which has a breaking stress of 8 × 10
8

N/m
2
. The area of cross-section of the upper wire is 0.006 cm
2
and that of the lower wire is 0.003
cm . The mass m 1 = 10 kg, m 2 = 20 kg and the hanger is light. Find the maximum load that can be
put on the hanger without breaking a wire. Which wire will break first if the load is increased ?
(Take g = 10 m/s
2
)

Q 6.  A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end
and the combination is subjected to a tension. Find the ratio of:

(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 10
11
N/m
2
and T of copper = 1.3 × 10
11
N/m
2
)
Q 7.  Calculate the approximate change in density of water in a lake at a depth of 400 m below the
surface. The density of water at the surface is 1030 kg/m
3
and bulk modulus of water is 2 ×
10
9
N/m
2
.
Q 8.  A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 10
10
N/m
2
is suspended from a
point and supports a heavy cylinder of volume 10
-3
m
3
at its lower end. Find the decrease in length
when the metal cylinder is immersed in a liquid of density 800 kg/m
3
.
Q 9.  In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction
in the volume of the ball is 0.1%. The density of water of the lake is 1 × 10
3
kg/m . Determine the
value of the bulk modulus of elasticity of rubber. (g = 9.8m/s
2
)
Q 10.  A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m
and diameter 4 mm which is suspended from the ceiling of a room. The point of support is 521 cm
above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes
the floor. Calculate the velocity of the ball at its lowest position. (Y steel =2 × 10
11
N/m
2
)
axis with a frequency v. If density of the wire is p and Young's modulus is Y. Find the fractional
change in radius of the ring.
Q 12.  A 6 kg weight is fastened to the end of a steel wire of unstretched length 60 cm. It is whirled in a
vertical circle and has an angular velocity of 2 rev's at the bottom of the circle. The area of cross-
section of the wire is 0.05 cm
2
. Calculate the elongation of the wire when the weight is at the
lowest point of the path. Young's modulus of steel =2 × 10
11
N/m
2
.
Q 13.  A homogeneous block with a mass m hangs on three vertical wires of equal length arranged
symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of
copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be
double than that of copper.

Q 14.  A uniform copper bar of density length L, cross-sectional area S and Young's modulus Y is
moving horizontally on a frictionless surface with constant acceleration a0. Find :
(a) the stress at the centre of the wire, (b) total elongation of the wire.
Q 15.  A 5 m long cylindrical steel wire with radius 2 × 10
-3
m is suspended vertically from a rigid
support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the
change in temperature of the wire ignoring radiation losses. (Take g =10m/s
2
)
(For the steel wire : Young's modulus =2.1 × 10
11
N/m
2
; Density = 7860 kg/m
3
; Specific heat =
420.T/kg-°C).
Solutions
1.

= 1.9 × 10
-3
m = 1.9 mm
2.  × 3 × 10
8
N/m
2

3.

4.

= 49 × 10
-6
m
5.

= 48 - 30 = 18 kg

So, lower wire will break if m > 14 kg. i.e., maximum load which can be put on hanger without
breaking wire is 14 kg
6.   is same as both have same cross-section area and subjected under same tension.

7.
Page 4

EXERCISES
For JEE Main
Subjective Questions
Q 1.  A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400
N is applied to each end of the wire. What minimum diameter is required for the wire ?
Ysteel =2.1 × 10
11
N/m
2

Q 2.  The elastic limit of a steel cable is 3.0 × 10
8
N/m
2
and the cross-section area is 4 cm
2
. Find the
maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the
stress is not to exceed one-third of the elastic limit.
Q 3.  If the elastic limit of copper is 1.5 x 10
8
N/m
2
, determine the minimum diameter a copper wire can
have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Q 4.  Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own
weight. Density of steel = 8000 kg/m
3
and Young's modulus of steel = 2 x 10
11
N/m
2
. What is the
energy stored in the wire ? (Take g = 9.8m/s
2
)
Q 5.  Two wires shown in figure are made of the same material which has a breaking stress of 8 × 10
8

N/m
2
. The area of cross-section of the upper wire is 0.006 cm
2
and that of the lower wire is 0.003
cm . The mass m 1 = 10 kg, m 2 = 20 kg and the hanger is light. Find the maximum load that can be
put on the hanger without breaking a wire. Which wire will break first if the load is increased ?
(Take g = 10 m/s
2
)

Q 6.  A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end
and the combination is subjected to a tension. Find the ratio of:

(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 10
11
N/m
2
and T of copper = 1.3 × 10
11
N/m
2
)
Q 7.  Calculate the approximate change in density of water in a lake at a depth of 400 m below the
surface. The density of water at the surface is 1030 kg/m
3
and bulk modulus of water is 2 ×
10
9
N/m
2
.
Q 8.  A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 10
10
N/m
2
is suspended from a
point and supports a heavy cylinder of volume 10
-3
m
3
at its lower end. Find the decrease in length
when the metal cylinder is immersed in a liquid of density 800 kg/m
3
.
Q 9.  In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction
in the volume of the ball is 0.1%. The density of water of the lake is 1 × 10
3
kg/m . Determine the
value of the bulk modulus of elasticity of rubber. (g = 9.8m/s
2
)
Q 10.  A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m
and diameter 4 mm which is suspended from the ceiling of a room. The point of support is 521 cm
above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes
the floor. Calculate the velocity of the ball at its lowest position. (Y steel =2 × 10
11
N/m
2
)
axis with a frequency v. If density of the wire is p and Young's modulus is Y. Find the fractional
change in radius of the ring.
Q 12.  A 6 kg weight is fastened to the end of a steel wire of unstretched length 60 cm. It is whirled in a
vertical circle and has an angular velocity of 2 rev's at the bottom of the circle. The area of cross-
section of the wire is 0.05 cm
2
. Calculate the elongation of the wire when the weight is at the
lowest point of the path. Young's modulus of steel =2 × 10
11
N/m
2
.
Q 13.  A homogeneous block with a mass m hangs on three vertical wires of equal length arranged
symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of
copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be
double than that of copper.

Q 14.  A uniform copper bar of density length L, cross-sectional area S and Young's modulus Y is
moving horizontally on a frictionless surface with constant acceleration a0. Find :
(a) the stress at the centre of the wire, (b) total elongation of the wire.
Q 15.  A 5 m long cylindrical steel wire with radius 2 × 10
-3
m is suspended vertically from a rigid
support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the
change in temperature of the wire ignoring radiation losses. (Take g =10m/s
2
)
(For the steel wire : Young's modulus =2.1 × 10
11
N/m
2
; Density = 7860 kg/m
3
; Specific heat =
420.T/kg-°C).
Solutions
1.

= 1.9 × 10
-3
m = 1.9 mm
2.  × 3 × 10
8
N/m
2

3.

4.

= 49 × 10
-6
m
5.

= 48 - 30 = 18 kg

So, lower wire will break if m > 14 kg. i.e., maximum load which can be put on hanger without
breaking wire is 14 kg
6.   is same as both have same cross-section area and subjected under same tension.

7.

8.

= -2.39 × 10
-3
m
9.
= 1.76 × 10
9
N/m
2
10.

11.
sin ? ? ?

= 2 ? v
2
mR

l = 2 ?R

But m = (2 ?R)( ?r
2
)( ?)
Page 5

EXERCISES
For JEE Main
Subjective Questions
Q 1.  A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400
N is applied to each end of the wire. What minimum diameter is required for the wire ?
Ysteel =2.1 × 10
11
N/m
2

Q 2.  The elastic limit of a steel cable is 3.0 × 10
8
N/m
2
and the cross-section area is 4 cm
2
. Find the
maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the
stress is not to exceed one-third of the elastic limit.
Q 3.  If the elastic limit of copper is 1.5 x 10
8
N/m
2
, determine the minimum diameter a copper wire can
have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Q 4.  Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own
weight. Density of steel = 8000 kg/m
3
and Young's modulus of steel = 2 x 10
11
N/m
2
. What is the
energy stored in the wire ? (Take g = 9.8m/s
2
)
Q 5.  Two wires shown in figure are made of the same material which has a breaking stress of 8 × 10
8

N/m
2
. The area of cross-section of the upper wire is 0.006 cm
2
and that of the lower wire is 0.003
cm . The mass m 1 = 10 kg, m 2 = 20 kg and the hanger is light. Find the maximum load that can be
put on the hanger without breaking a wire. Which wire will break first if the load is increased ?
(Take g = 10 m/s
2
)

Q 6.  A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end
and the combination is subjected to a tension. Find the ratio of:

(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 10
11
N/m
2
and T of copper = 1.3 × 10
11
N/m
2
)
Q 7.  Calculate the approximate change in density of water in a lake at a depth of 400 m below the
surface. The density of water at the surface is 1030 kg/m
3
and bulk modulus of water is 2 ×
10
9
N/m
2
.
Q 8.  A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 10
10
N/m
2
is suspended from a
point and supports a heavy cylinder of volume 10
-3
m
3
at its lower end. Find the decrease in length
when the metal cylinder is immersed in a liquid of density 800 kg/m
3
.
Q 9.  In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction
in the volume of the ball is 0.1%. The density of water of the lake is 1 × 10
3
kg/m . Determine the
value of the bulk modulus of elasticity of rubber. (g = 9.8m/s
2
)
Q 10.  A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m
and diameter 4 mm which is suspended from the ceiling of a room. The point of support is 521 cm
above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes
the floor. Calculate the velocity of the ball at its lowest position. (Y steel =2 × 10
11
N/m
2
)
axis with a frequency v. If density of the wire is p and Young's modulus is Y. Find the fractional
change in radius of the ring.
Q 12.  A 6 kg weight is fastened to the end of a steel wire of unstretched length 60 cm. It is whirled in a
vertical circle and has an angular velocity of 2 rev's at the bottom of the circle. The area of cross-
section of the wire is 0.05 cm
2
. Calculate the elongation of the wire when the weight is at the
lowest point of the path. Young's modulus of steel =2 × 10
11
N/m
2
.
Q 13.  A homogeneous block with a mass m hangs on three vertical wires of equal length arranged
symmetrically. Find the tension of the wires if the middle wire is of steel and the other two are of
copper. All the wires have the same cross-section. Consider the modulus of elasticity of steel to be
double than that of copper.

Q 14.  A uniform copper bar of density length L, cross-sectional area S and Young's modulus Y is
moving horizontally on a frictionless surface with constant acceleration a0. Find :
(a) the stress at the centre of the wire, (b) total elongation of the wire.
Q 15.  A 5 m long cylindrical steel wire with radius 2 × 10
-3
m is suspended vertically from a rigid
support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the
change in temperature of the wire ignoring radiation losses. (Take g =10m/s
2
)
(For the steel wire : Young's modulus =2.1 × 10
11
N/m
2
; Density = 7860 kg/m
3
; Specific heat =
420.T/kg-°C).
Solutions
1.

= 1.9 × 10
-3
m = 1.9 mm
2.  × 3 × 10
8
N/m
2

3.

4.

= 49 × 10
-6
m
5.

= 48 - 30 = 18 kg

So, lower wire will break if m > 14 kg. i.e., maximum load which can be put on hanger without
breaking wire is 14 kg
6.   is same as both have same cross-section area and subjected under same tension.

7.

8.

= -2.39 × 10
-3
m
9.
= 1.76 × 10
9
N/m
2
10.

11.
sin ? ? ?

= 2 ? v
2
mR

l = 2 ?R

But m = (2 ?R)( ?r
2
)( ?)
Substituting

the values we get,

12.

= 3.8 × 10
-4
m
13.  2Tc + T s = mg    ...(i)

Solving these two equations we get,

14.
(a) At centre :

?  Stress =
(b) At distance x from end B :
Tx =m xa0 =(xs ?)a0

15.  Energy stored in stretched wire = ms ?Q

Objective Questions Single Correct Option
Q 1.  The bulk modulus for an incompressible liquid is
(a) zero   (b) unity   (c) infinity   (d) between 0 and 1
Q 2.  The Young's modulus of a wire of length (L) and radius (r) is 7. If the length is reduced to
L
2
and
r
2
,

then its Young's modulus will be
(a)
Y
2
(b) 7    (c) 27    (d) 47
Q 3.  The maximum load that a wire can sustain is W. If the wire is cut to half its value, the maximum
(a) W    (b)
W
2
(c)
W
4
(d) 2W
Q 4.  Identify the case when an elastic metal rod does not undergo elongation
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