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

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 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. $4.5\times {10}^{11}$ $J$