A wire is stretched by hanging a weight from its end and develops a longitudinal strain ${\sigma }_1$, Y being the Young's modulus, elastic potential energy of the wire per unit volume can be expressed as: 

• A

  $\frac{Y{\sigma }_l}{2}$

• B

  $\frac{{\mathrm{Y\sigma }}_{\mathrm{l}}^2}{2}$

• C

  $\frac{3{\mathrm{Y\sigma }}_{\mathrm{l}}^2}{2}$

• D

  $\frac{{\mathrm{Y\sigma }}_{\mathrm{l}}^2}{4}$