$\frac{\text { Lateral strain }}{\text { Longitudinal strain }}=$ Poisson's ratio

$\frac{0.02 / 100}{\Delta l / l}=\frac{1}{4}$  $\left\{\begin{array}{l}Y=\text { (Young's modulus) } \\ \quad=8 \times 10^{10} \text { (given) } \\ \text { Poission's ratio }=\frac{1}{4} \text { (given) } \\ \text { Lateral strain }=0.02 \% \text { (given) }\end{array}\right.$

$\frac{\Delta l}{l}=\frac{0.08}{100}$

$\Delta U$ (Elastic potential energy per unit volume $=\frac{1}{2} \times Y \times($ Longitudinal strain $\left.)\right)$

Substituting values

$\Delta U=\frac{1}{2} \times 8 \times 10^{10} \times\left(\frac{0.08}{100}\right)^2$

$\Delta U=2.56 \times 10^4 \,J / m ^3$