Q 11-10-091JEE MainJEE Main 2021 (22 Jul, Shift 1)Medium
The area of cross-section of a railway track is $0.01\ \text{m}^2$. The temperature variation is 10 °C. Coefficient of linear expansion of material of track is $10^{-5}\ °\text{C}^{-1}$. The energy stored per meter in the track is ______ $\text{J m}^{-1}$. (Young's modulus of material of track is $10^{11}\ \text{N m}^{-2}$)
Numerical value type. Enter your answer.
Answer: 5
Thermal stress: $\sigma = Y\alpha\Delta T = 10^{11}\times10^{-5}\times10 = 10^7$ Pa.
Energy per unit volume $= \dfrac{\sigma^2}{2Y} = \dfrac{10^{14}}{2\times10^{11}} = 500\ \text{J m}^{-3}$.
Per metre of track: $500\times0.01 = 5\ \text{J m}^{-1}$.
Solution by Sreeraj P, M.Sc Physics