The work done in stretching an elastic wire per unit volume is or strain energy in a stretched string is

1. Stress $\times$ Strain                     

2. $\frac{1}{2}\times$ Stress $\times$Strain

3. $2\times strain\times stress$                   

4. Stress/Strain

The elastic energy stored in a wire of Young's Modulus Y is -

1. $\mathrm{Y}\times \frac{{\mathrm{strain}}^2}{\mathrm{volume}}$

2. $\mathrm{stress}\times \mathrm{strain}\times \mathrm{volume}$

3. $\frac{{\mathrm{strain}}^2\times \mathrm{volume}}{2\mathrm{Y}}$

4. $\frac{1}{2}\times stress\times strain\times volume$

If Y represents Young's modulus of elasticity and $\mathrm{\epsilon }$ represents the longitudinal strain, the energy stored per unit volume of a stretched wire is:

1.  $\frac{1}{2}\mathrm{Y\epsilon }$

2.  $\frac{1}{2}{\mathrm{Y}}^2\mathrm{\epsilon }$

3.  $\frac{1}{2}{\mathrm{Y\epsilon }}^2$

4.  $\frac{1}{2}{\mathrm{Y}}^2{\mathrm{\epsilon }}^2$

If x longitudinal strain is produced in a wire of Young's modulus y, then energy stored in the material of the wire per unit volume is-

1. $y{x}^2$

2. $2y{x}^2$  

3. $\frac{1}{2}{y}^{2}x$

4. $\frac{1}{2}y{x}^2$ 

The elastic energy stored in a wire of Young's Modulus Y is -

1. $\mathrm{Y}\times \frac{{\mathrm{strain}}^2}{\mathrm{volume}}$

2. $\mathrm{stress}\times \mathrm{strain}\times \mathrm{volume}$

3. $\frac{{\mathrm{strain}}^2\times \mathrm{volume}}{2\mathrm{Y}}$

4. $\frac{1}{2}\times stress\times strain\times volume$

A wire of length L and area of cross-section A is made of material of Young's modulus Y. If its length is stretched by x, the work done is:

1.  $\frac{{\mathrm{YAx}}^2}{\mathrm{L}}$

2.  $\frac{{\mathrm{YAx}}^2}{2\mathrm{L}}$

3.  $\frac{2{\mathrm{YAx}}^2}{\mathrm{L}}$

4.  $\frac{\mathrm{YAx}}{2\mathrm{L}}$