Two parallel steel wires A and B are fixed to rigid support at the upper ends and subjected to the same load at the lower ands. The lengths of wires are in the ratio 4:5 and their radii are in the ratio 4:3. The increase in the length of the wire A is 1mm. Calculate the increase in the length of the wire B.

3

(a)

Determine the volume contraction of a solid copper cube, 10cm on an edge, when subjected to a hydraulic pressure of 7 x 10⁶ Pa. Bulk modulus for copper = 140 x 10⁹ Pa.

3

(a)

Read the following two statements below carefully and state, with reasons, if it is true or false.
(a) The Young’s modulus of rubber is greater than that of steel;
(b) The stretching of a coil is determined by its shear modulus.

3

(a)

A steel wire of length 4 m is stretched through 2 mm. The cross-section area of the wire is 2.0 mm². If Young's modulus of steel is 2.0 x 10¹¹ N/m², find
(i) the energy density of the wire and
(ii) the elastic potential energy stored in the wire.

3

(a)

Explain why steel is more elastic than rubber.

3

(a)

Why are the springs made of steel and not of copper?

3

(a)

A solid sphere of radius 10 cm is subjected to a uniform pressure equal to 5 x 10⁸ Nm^-2. Calculate the change in volume. Bulk modulus of the material of the sphere is 3.14 x 10¹¹ Nm^-2.

3

(a)

The length of a metal wire is l₁ when the tension in it is T₁ and is l₂when the tension is T₂· Find the original length of the wire.

3

(a)

Elasticity is said to be internal property of matter. Explain.

3

(a)

Two wires A and B of length, l radius r and length 2l, radius 2r having same Young's modulus \(\Upsilon \) are hung with a weight mg, see fig. What is the net elongation in the two wires?

3

(a)

A 4 m long aluminium wire whose diameter is 3 mm is used to support a mass of 50 kg. What will be the elongation of the wire? \(\Upsilon \) for aluminium is 7 x 10¹⁰ Nm^-2. Given: g = 9.8 ms^-2.

3

(a)

Calculate the force required to punch a hole 2 cm square in a steel sheet 2 mm thick whose shearing strength is 3.5 x 10⁸ Nm^-2.

3

(a)

What is an elastomer? What are their special features?

3

(a)

What do you mean by compressibility? Why are solids least compressible and gases most compressible?

3

(a)

What is elastic hysteresis?

3

(a)