1. A mass of 5000 kg is supported on a column 0.02 m × 0.02 m.

What is the stress in the column

2. When a load of 3 kg is attached to the free end of a suspended wire of length 5 m and diameter 2
mm, the elongation produced is 0.5 mm. Calculate the i) longitudinal stress, ii) longitudinal
strain and iii) Young’s modulus of the material of the wire.

3. There are two wires of the same material. Their radii and the length are both in the ratio 1: 2. If
the extension produced are equal, what is the ratio of loads?

4. Prove that the stress needed to double the length of a wire of uniform cross section is equal to its
Young’s modulus. Assume that Hooke’s law is obeyed during the extension of the wire.

5. Young’s modulus of the material of a wire is 9.68 × 10 10 N/m2. A wire of material of diameter
0.95 mm is stretched by applying a certain force. What should be the limit of this force, if the
strain is not to exceed 1 in 1000?

6. A copper wire and a steel wire each of the same length and cross section are joined end to end.
The composite wire is hung from a rigid support and load is suspended from the other end. If the
increase in length of the steel wire is 0.6 mm. Find the increase in length of the composite wire.

Given : Ycu = 1.2 × 1011 N/m2,

Ysteel = 2 × 1011 N/m2

7. A steel wire of length 2 m and an area of cross section of 0.5 mm 2 is fixed at one end to a rigid
support and a steel block of volume 500 cm 3 is suspended from the other end. When the block is
completely immersed in water, the wire contract in length by 9.8 × 10 -2 mm. Find the value of Y
for steel.

8. A steel wire of length 7 m and cross section 1 mm 2 is hung from a rigid support with a steel
weight of volume 1000 c.c. hanging from the other end. Find the decrease in length of wire when
steel weight is completely immersed in water.

(Y for steel = 2 × 1011 N/m2)

(Density of water = 1 gm/ c.c)

9. Calculate the stress applied to the wire having mass per unit length 0.1 gm/cm and density 7
gm/cm3, when 10 gm.wt is attached to its free end.

10. Show that the deforming force is directly proportional to the change in the volume of a sire in
case of Young’s modulus.

11. The elastic limit of copper is 1.5 ×10 4 N/m2. Find the minimum radius of a copper wire must
have, if its elastic limit is not to be exceeded under a load of 10 kg.

(g = 9.8 m/s2)
12. The Young’s modulus of a material of a rod is 200 GPa. Its coefficient of linear expansion is 15
× 10-6 /0 C. It is fixed at two ends and is cooled by 100 0 C. Calculate the thermal stress produced
in the rod.

13. A steel wire of length 20 cm and cross sectional area 1 mm 2 is clamped at both the ends. The
coefficient of linear expansion for steel  = 1.1 × 10-5 /0C and Y = 2 × 10 11 N/m2. If the
temperature of wire is reduced from 400 C to 200 C, calculate the tension developed in the wire.

Problems for Practice

14. A load of 2000 kg is supported by a cylindrical column 0.1 m in diameter. What is the stress in
the column? (g = 9.8 m/s2)
Longitudinal stress
Formula: Longitudinal strain
15. A column 3 m long supporting the floors of a shop shortens by 0.015 × 10 -2 m, when a heavy
machine is installed. What is the strain in column.
F
A FL
= =
l Al
Formula : L

16. A wire of length 4 m and area of cross section 2 mm 2 is extended by 2 mm when stretching force
of 80 N is applied to it, calculate the tensile stress, strain and Young’s modulus of material of the
wire.
MgL
Y=
Formula: i) Tensile stress = πR2 l
(Los of weightof the¿) ¿
ii) Tensile strain = ¿
( Volume or ¿ ) ¿ ¿¿
iii) ¿
17. When a load of 5 kg wt is applied to the end of wire of length 1.5 m suspended from a rigid
support, the extension produced in it is 6 mm. If the diameter of wire is 3 × 10 -4 m. Find i)
longitudinal stress ii) longitudinal strain and iii) Young’s modulus. (g = 9.8 m/s 2)
( Volume or ¿ ) ¿ ¿¿
Formula: ¿ ,
dV
=
V
volume stress
volume strain
18. A metal wire of diameter 1 mm and length 2 m is stretched by applying a force of 2 kg wt.
Calculate the increase in length of wire strain and stress. (Y = 2 × 10 11 N/m2, g = 9.8 m/s2)
Formula: Stress = Mg/R2,
dP
K=
Strain = dV /V
 dP
K =V
dV
19. Stress applied to the wire is equal to its Young’s modulus. Find the change in length of wire in
terms of its original length.
1
Formula: K
20. A metal wire is observed to stretched by one part is a million when subjected to a stress of 8 × 10 4
N/m2. Calculate the Young’s modulus of the metal.
tan gential force
Formula: area
21. Young’s modulus of material of wire is 1.2 × 10 11 N/m2 . Calculate the radius of the wire, if the
load of 8 kg. wt produces and extension of 0.52 mm in a wire of length 2.5 cm.
F
Formula: A
22. A load of 2 kg is applied to the end of wire of length 2 m and diameter 2 × 10 -4 m suspended from
a rigid support. If Young’s modulus of material of the wire is 2 × 10 11 N/m2, find extension
produced in the wire.
( Lateraldisplacement¿) ¿¿¿¿¿
Formula: ¿
23. Young’s modulus of material of wire is 7 × 10 10 N/m2 . The wire is stretches by a load so that the
longitudinal strain produced in it is 5 × 10-3. Find the corresponding stress.
Formula: Stress = Y. Strain
24. The radius of wire is 4 mm. What force is required to stretch the wire by 20% of its length,
assuming that elastic limit is not exceeded? (Y = 12 × 10 10 N/m2)
Formula: F = Y A × Strain
25. A wire of radius 0.5 mm has an initial length of 1.2 m What force must be applied to the wire to
stretched it to a length of 1.21 m. (Y = 1.28 × 1011 N/m2)
Formula: F = A.Y Strain
x
=  R2 Y L
26. The radius of wire is 0.02 mm. Find the force required to produce an elongation of 0.2 % of the
initial length of the wire. (Y = 1.7 × 1011 N/m2)
27. Two wires have their lengths in the ratio 3:2, diameters in the ratio 2 : 1 and Young’s moduli in
the ratio 1:2. Calculate the ratio of elongations produced in the wires when they are subjected to
the same stretching force.
Shearing stress
Formula : Shearing strain
28. Two wires of the same material have lengths in the ratio 3 : 2 and diameters in the ratio 2:1.
Compare their extensions when the same load is applied to both the wires.
 F
A
η=
Formula: θ
29. The extension produced is a wire by certain load is 1 mm. Find the extension produced in the
wire of the same material but having a length 1.5 times and diameter 2 times that of the first wire,
when it is subjected to a load that is 3 times greater.
F
=
Formula: A⋅θ
30. A copper wire and steel wire of same length and cross sectional are joined end to end. The
composite wire is hung from a rigid support and a load is suspended from the free end. If the
increase in length of the copper wire is 2 mm. Find the increase in length of steel wire.
Ycu = 1.2 × 1011 N/m2 ,
Ysteel = 2 × 1011 N/m2
F
=
A⋅x
Formula : L
31. An aluminium wire and a steel wire of same length and cross section are joined end to end. The
composite wire is hung from a rigid support and a load is suspended from the free end. If the
increase is length of the composite wire 2.7 mm, find the increase in length of each wire.
(Yal = 7 × 1010 N/m2,
Ysteel = 2 × 1011 N/m2)
F⋅L
η=
Formula : A⋅x
l1 + l2 = 2.7 × 10-3
32. A copper wire and a steel wire both of same length and radius are joined end to end. The
composite wire is hung from a rigid support and a load is attached to free end. The increase in
length of composite wire is found to be 1 cm. Find the increase in lengths of copper and steel
wires.
Given: YC = 1.2 × 1011 N/m2.
YS = 2.1 × 1011 N/m2
change in diameter d
=
Formula: original diameter D
33. A copper wire and brass wire each of same cross section are joined end to end. The composite
wire is hung from a rigid support and a load is suspended from other end. If each wire undergoes
the same extension, find the ratio of length of copper segment to the length of brass segment.
(Ycu = 1.2 × 1011 N/m2, Yb = 9 × 1010 N/m2).
change in length l
=
Formula: originallength L
34. A metal wire of uniform cross section of 0.01 cm 2 is hung from a rigid support with a mass of
metal of volume 2000 cc hanging from the other end. When the mass is completely immersed in
water, the length of the wire changes by 1 mm. Find the unstretched length of the wire.
 (Given Y = 2 × 1011 N/m2, g = 9.8 m/s2 Density of water = 1g/cc)
Lateral strain
Formula: Longitudinal strain
d
D
σ =

Hint: l
L

35. The Young’s modulus of a material of a rod is 1.2 × 10 11 N/m2. Its coefficient of linear expansion
is 1.5 × 10-5 /0 C. It is fixed at two ends and is cooled by 70 0 C. Calculate the thermal stress
produced in the rod.
Formula: Thermal stress = Y  ∆
36. A steel wire of length 25 cm and cross – sectional area 10 mm 2 is clamped at both the ends. The
coefficient of linear expansion for steel  = 1.3 × 10-5/0C and Y = 1.7 × 1011 N/m2. If the
temperature of wire is reduced from 500 C to 200 C, calculate the tension developed in the wire.
Formula: F = YA  ∆