Q 11-08-107JEE MainJEE Main 2025 (2 Apr, Shift 1)Medium
A steel wire of length $2\ \text{m}$ and Young's modulus $2.0\times10^{11}\ \text{N m}^{-2}$ is stretched by a force. If the Poisson ratio and transverse strain for the wire are $0.2$ and $10^{-3}$ respectively, then the elastic potential energy density of the wire is ______ $\times10^5$ (in SI units).
Numerical value type. Enter your answer.
Answer: 25
Poisson's ratio = transverse strain / longitudinal strain, so
$$\varepsilon_\ell = \frac{10^{-3}}{0.2} = 5\times10^{-3}$$
Energy per unit volume:
$$u = \tfrac12 Y\varepsilon_\ell^2 = \tfrac12\times2\times10^{11}\times(5\times10^{-3})^2 = 25\times10^5\ \text{J/m}^3$$
Solution by Sreeraj P, M.Sc Physics