Mechanical Properties of Solids
Q 1 Define stress.
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Q 2 What is the dimensional formula of young’s modulus of elasticity?
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Q 3 What is the value of young’s modulus for a perfectly rigid body?
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Q 4 Why young’s modulus and shear modulus are relevant only for solids?
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Q 5 What is the value of modulus of rigidity for a liquid?
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Q 6 A wire 3 m in length suspended vertically stretches by 1 mm when mass of 40 kg is
attached to the lower end. What is the potential energy gained by the wire?
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Q 7 What is an elastic limit?
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Q 8 Define shear strain.
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Q 9 What is compressibility?
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Q 10 Two wires of same material and length are stretched by the same force. Their
masses are in the ratio 3:2. Find the ratio of their elongations.
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Q 11 The young’s modulus of the material of a wire is 6
transverse strain in it. Find its modulus of rigidity?
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1012N/m2 and there is no
Q 12 Explain why solids are more elastic than gases?
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Q 13 A rod elongates by l when a body of mass m is suspended from it. Find the work
done in the process?
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Q 14 The breaking stress of aluminium is 8.1 107Nm-2. Find the greatest length of
aluminium wire that can hang vertically without breaking. Density of aluminium is 2.7
103 kgm-3.
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Q 15 Two wires A and B of the same material have radii in the ratio 2:1 and lengths in
the ratio 4:1. Find the ratio of the normal forces required to produce the same change in
the lengths of the two wires?
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Q 16 Find the maximum length of steel wire that can hang without breaking. Breaking
stress=7.9 1012dyne/cm2. Density of steel =7.9g/cc
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Q 17 The ratio of radii of two wires of same material is 2:1. If these wires are stretched
by equal force, find the ratio of stresses produced in them.
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Q 18 A long spring is stretched by 2 cm and its potential energy is V. Find the potential
energy of the spring if it is stretched by 10 cm?
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Q 19
Forces of 105N each are applied in opposite directions on upper and lower faces of a cube
of side 10cm, shifting the upper face parallel to itself by 0.5cm. If the side of the cube
were 20cm, what would be the displacement?
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Q 20 A copper and a steel wire of same length and cross section are attached end to end.
The compound wire is hung from a rigid support and a load is suspended from the free
end. If Y of steel is (20/9) times of copper then find the ratio of increase in length of steel
wire to copper wire?
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Q 21 Compute the fractional change in volume of a glass slab, when subjected to a
hydraulic pressure of 1 atm. It is given bulk modulus of glass = 37X109Nm-2
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Q 22 One end of a steel wire is fixed to the ceiling of an elevator moving up with an
acceleration of 2m/s2 and a load of 10 kg hangs from other end. Area of cross section of
the wire is 2cm2. Find the longitudinal strain in the wire? Y=2 1011N/m2
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Q 23 The length of a wire increases by 8 mm when a weight of 5 kg is hung. If the radius
of the wire is doubled, what will be the increase in length?
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Q 24 A spherical ball contracts in volume by 0.01% when subjected to a normal uniform
pressure of 100 atm. Calculate the bulk modulus of the material.
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Q 25 Read each of the statements below carefully and state, with reasons, if it is true or
false?
(a) The modulus of elasticity of rubber is greater than that of steel.
(b) The stretching of a coil is determined by its shear modulus.
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Q 26 A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1m, is
whirled in a vertical circle with an angular velocity of 2 rev/sec at the bottom of the
circle. The cross sectional area of the wire is 0.065cm2. Calculate the elongation of the
wire when the mass is at the lowest point of its path. Ysteel=2 1011N/m2
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Q 27 One end of a wire 2m long and diameter 2mm is fixed in the ceiling. A naughty boy
of mass 10kg jumps to catch the free end and stays there. Find the change in the length of
the wire. Y=2 1011N/m2
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Q 28 A wire of length ‘L’ and area of cross section ‘A’ is made of material of young’s
modulus ‘Y’. Find the work done if it is stretched by an amount ‘x’ ?
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Q 29 A copper wire of length 4.8m and cross section 2.0 10-5m2 stretches by the same
amount as a steel wire of length 1.6m and area of cross section 4 10-5m2 under a given
load. What is the ratio of the young’s modulus of copper to that of steel ?
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