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 $6\times {10}^{12}N/m^2$ and  there is no transverse strain in it, then its modulus of rigidity will be

(1) $3\times {10}^{12}N/m^2$                       

(2) $2\times {10}^{12}N/m^2$

(3) ${10}^{12}N/m^2$                             

(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 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

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 -

(a) 34 m                             (b) 30 m

(c) 300 m                            (d) 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 3L/4 from its lower end is

1. $\frac{W_1}{S}$                     

2. $\frac{W_1+\left(W/4\right)}{S}$

3. $\frac{W_1+\left(3W/4\right)}{S}$

4. $\frac{W_1+W}{S}$