The work done in stretching an elastic wire per unit volume is:

An elastic material of Young's modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is:

1. $\frac{SY}{2}$ $$ $$

2. $\frac{S^2}{2Y}$

3. $\frac{S}{2Y}$ $$

4. $\frac{2S}{Y}$

If \(\mathrm{E}\) is the energy stored per unit volume in a wire having \(\mathrm{Y}\) as Young's modulus of the material, then the stress applied is:
1. $\sqrt{2\mathrm{EY}}$

2. $2\sqrt{\mathrm{EY}}$

3. $\frac{1}{2}\sqrt{\mathrm{EY}}$

4. $\frac{3}{2}\sqrt{\mathrm{EY}}$

The Young's modulus of a wire is Y.  If the energy per unit volume is E, then the strain will be:

1. $\sqrt{\frac{2E}{Y}}$                                         

2. $\sqrt{2EY}$

3. $EY$                                             

4. $\frac{E}{Y}$

A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:
1. $\frac{YxA}{2L}$

2. $\frac{Y{x}^{2}A}{L}$

3. $\frac{Y{x}^{2}A}{2L}$

4. $\frac{2Y{x}^{2}A}{L}$

A \(5\) m long wire is fixed to the ceiling. A weight of \(10\) kg is hung at the lower end and is \(1\) m above the floor. The wire was elongated by \(1\) mm. The energy stored in the wire due to stretching is:
1. zero                                 
2. \(0.05\) J
3. \(100\) J                          
4. \(500\) J

The ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be:

1. 3 : 2                                   

2. 2 : 3

3. 3 : 4                                   

4. 4 : 3

The work done per unit volume to stretch the length of a wire by 1%  with a constant cross-sectional area will be: $\left[Y=9\times {10}^{11}N/m^2\right]$

1. $9\times {10}^{11}$ $J$

2. $4.5\times {10}^{7}J$

3. $9\times {10}^{7}J$

4. $4.5\times {10}^{11}$ $J$

If the force constant of a wire is K, the work done in increasing the length of the wire by l is:

1. $Kl/2$                                   

2. $Kl$

3. $K{l}^2/2$                                 

4. $K{l}^2$

A wire of negligible mass and length 2 m is stretched by hanging a 20 kg load to its lower end keeping its upper end fixed. If work done in stretching the wire is 50 J, then the strain produced in the wire will be:

1. 0.5

2. 0.1

3. 0.4

4. 0.25