The Young's modulus of a rubber string 8 cm long and density $1.5 kg/m^3$ is $5\times {10}^8 N/m^2$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

1. $9.6\times {10}^{-5} m$                           

2. $9.6\times {10}^{-11}m$

3. $9.6\times {10}^{-3} m$                           

4. 9.6 m

A and B are two wires of same material. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is

1. Equal to that on A

2. Four times that on A

3. Two times that on A               

4. Half that on A

If the length of a wire is reduced to half, then it can hold the ......... load

1. Half                                 

2. Same

3. Double                             

4. One fourth

Why the spring is made up of steel in comparison of copper?

1. Copper is more costly than steel

2. Copper is more elastic than steel

3. Steel is more elastic than copper

4. None of the above

Two wires of copper having length in the ratio of \(4:1\) and radii ratio of \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two will be:

The force constant of a wire does not depend on

1. Nature of the material                     

2. Radius of the wire

3. Length of the wire                           

4. None of the above

The quality of the material which opposes the change in shape, volume or length is called

1.   Intermolecular repulsion

2.   Intermolecular behaviour

3.   Viscosity

4.   Elasticity

A wire of length L and radius r is  rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

1. l                                       
2. 2l
3. $\frac{l}{2}$                                   
4. $\frac{l}{4}$ 

In steel, the Young's modulus and the strain at the breaking point are $2\times {10}^{11}N{m}^{-2}$ and 0.15 respectively. The stress at the breaking point for steel is therefore -

1. $1.33\times {10}^{11}N{m}^{-2}$           

2. $1.33\times {10}^{12}N{m}^{-2}$

3. $7.5\times {10}^{-13}N{m}^{-2}$           

4. $3\times {10}^{10}N{m}^{-2}$