A steel wire is fixed at its one end on the roof. At other ends of the wire, 1 kg mass is hanged so that the energy stored in the wire is E. The energy stored in the same wire if we hang 2 kg mass instead of 1 kg is:

(1) 2E

(2) 4E

(3) 8E

(4) E

The bulk modulus of a rubber ball is $9\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$. To what depth below the surface of the sea, should the ball be taken so as to decrease its volume by 0.1%?

(1) 1 m

(2) 10 m

(3) 90 m

(4) 1 km

What is the value of Poisson's ratio for an incompressible material?

(1) Zero

(2) 0.2

(3) 0.5

(4) Infinite

If the Poisson's ratio of a material is 0.5, then its bulk modulus is equal to:

(1) Zero

(2) Young's modulus

(3) Infinite

(4) Three times Young's modulus

A uniform wire of cross-sectional area A is stretched by a certain force so that its length is elongated by x. What should be the cross-sectional area of the wire, so that elongation becomes $\frac{\mathrm{x}}{2}$ on applying the same force?

(1) A

(2) 2A

(3) 4A

(4) 8A

A wire suspended vertically from one of its ends is stretched by attaching a weight of 100 N. If the elastic energy stored in the wire is 0.1 J. The elongation in the wire is:

(1) 1 mm

(2) 2 mm

(3) 3 mm

(4) 4 mm

Breaking stress of a wire of length L and radius r is B. If another wire made of the same material has length 2L and radius 2r, its breaking stress will be:

(1) 2B

(2) $\frac{\mathrm{B}}{4}$

(3) B

(4) 4B

If E is the energy stored per unit volume in a wire having Young's modulus of the material Y, then stress applied is:

1.  $\sqrt{2\mathrm{EY}}$

2.  $2\sqrt{\mathrm{EY}}$

3.  $\frac{1}{2}\sqrt{\mathrm{EY}}$

4.  $\frac{3}{2}\sqrt{\mathrm{EY}}$

Two wires of the same material have lengths in the ratio of 1: 2. If they are stretched by applying equal forces, the increase in lengths is the same. The ratio of their respective radii is:

(1) 1: 1

(2) 1: 2

(3) 1: $\sqrt{2}$

(4) 2: 1

The value of Poisson's ratio cannot be:

(1) 0.05

(2) 0.32

(3) 0.63

(4) 0.49