\(\frac{\text { Lateral strain }}{\text { Longitudinal strain }}=\) 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

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

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