The Young's modulus of a wire of length 'L' and radius 'r' is 'Y'. If length is reduced to L/2 and radius r/2, then Young's modulus will be 

1. Y/2

2. Y

3. 2Y

4. 4Y

Three wires \(A,B,C\) made of the same material and radius have different lengths. The graphs in the figure show the elongation-load variation. The longest wire is:
                    
1. \(A\)
2. \(B\)
3. \(C\)
4. All of the above

If Young modulus (Y) equal to bulk modulus (B). Then the Poisson ratio is :

1. $\frac{1}{3}$

2. $\frac{2}{3}$

3. $\frac{1}{2}$

4. $\frac{1}{4}$

When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, then the increase in length will be -

1. 0.5 cm                             

2. 2 cm

3. 4 cm                                 

4. 8 cm

A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be:

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

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

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:

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. $3\times {10}^{10}N{m}^{-2}$