Physics Question from JEE Main 2025 · 2 April, Shift 1

A steel wire of length $2 \, \text{m}$ and Young's modulus $2.0 \times 10^{11} \, \text{N/m}^2$ is stretched by a force. If Poisson's ratio and transverse strain for the wire are $0.2$ and $10^{-3}$ respectively, then the elastic potential energy density of the wire is _____ $\times 10^5$ (in SI units).