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

One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(S\) is the area of cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W_1}{S}\)
2. \(\frac{W_1+\left(\frac{W}{4}\right)}{S}\)
3. \(\frac{W_1+\left(\frac{3W}{4}\right)}{S}\)
4. \(\frac{W_1+W}{S}\)