Q 11-08-068JEE MainJEE Main 2022 (26 Jun, Shift 1)Medium
The elastic behaviour of a material for linear stress and linear strain is shown in the figure. The energy density for a linear strain of $5\times10^{-4}$ is ______ $\text{kJ m}^{-3}$. Assume that the material is elastic up to the linear strain of $5\times10^{-4}$.
Numerical value type. Enter your answer.
Answer: 25
From the graph, $Y = \dfrac{\text{stress}}{\text{strain}} = \dfrac{20}{10^{-10}} = 2\times10^{11}\ \text{Pa}$.
$$u = \frac12Y(\text{strain})^2 = \frac12\times2\times10^{11}\times(5\times10^{-4})^2 = 2.5\times10^4\ \text{J m}^{-3} = 25\ \text{kJ m}^{-3}$$
Solution by Sreeraj P, M.Sc Physics