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:

1.	$4:1$	2.	$16:1$
3.	$8:1$	4.	$1:1$

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 

1.  $\theta /4$                         
2. $\theta /2$
3. $5\theta /6$                       
4. $8\theta /9$

Shearing stress causes a change in-

1.   Length                              

2.   Breadth

3.   Shape                               

4.   Volume

To break a wire, a force of ${10}^{6}N/m^2$ is required. If the density of the material is $3\times {10}^3 kg/m^3$, then the length of the wire which will break by its own weight will be -

1. 34 m                             
2. 30 m
3. 300 m                          
4. 3 m

The strain-stress curves of three wires of different materials are shown in the figure. $P$, $Q$ and $R$ are the elastic limits of the wires. The figure shows that: