A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball

(1) $19.6\times {10}^{8}N/m^2$               

(2) $19.6\times {10}^{-10}N/m^2$

(3) $19.6\times {10}^{10}N/m^2$               

(4) $19.6\times {10}^{-8}N/m^2$

The Bulk modulus for an incompressible liquid is

(1) Zero                                           

(2) Unity

(3) Infinity                                       

(4) Between 0 to 1

The ratio of lengths of two rods \(A\) and \(B\) of the same material is \(1:2\) and the ratio of their radii is \(2:1\). The ratio of modulus of rigidity of \(A\) and \(B\) will be:

When a spiral spring is stretched by suspending a load on it, the strain produced is called:

The Young's modulus of the material of a wire is \(6\times 10^{12}~\text{N/m}^2\) and there is no transverse strain in it, then its modulus of rigidity will be:

1. \(3\times 10^{12}~\text{N/m}^2\)
2. \(2\times 10^{12}~\text{N/m}^2\)
3. \(10^{12}~\text{N/m}^2\)
4. None of the above

Modulus of rigidity of a liquid:

(1) Non zero constant

(2) Infinite

(3) Zero

(4) Can not be predicted

A cube of aluminium of sides \(0.1~\text{m}\) is subjected to a shearing force of \(100\) N. The top face of the cube is displaced through \(0.02\) cm with respect to the bottom face. The shearing strain would be:
1. \(0.02\)                                   
2. \(0.1\)
3. \(0.005\)                               
4. \(0.002\)

The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30°. Then angle of shear is

(1) $12°$                                     

(2) $0.12°$

(3) $1.2°$                                     

(4) $0.012°$

A rod of length l and radius r is joined to a rod of length l/2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $\theta$, the twist angle at the joint will be 

(a) $\theta /4$                          (b) $\theta /2$

(c) $5\theta /6$                         (d) $8\theta /9$

Shearing stress causes a change in-

(1)   Length                              

(2)   Breadth

(3)   Shape                               

(4)   Volume