JEE Main 2023 — Thermal Properties of Matter Question with Solution

A thin rod having a length of $1 \mathrm{m}$ and area of cross-section $3\times {10}^{-6} {\mathrm{m}}^2$ is suspended vertically from one end. The rod is cooled from $210°\mathrm{C}$ to $160°\mathrm{C}$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1 \mathrm{m}$. Young's modulus and coefficient of linear expansion of the rod are $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and $2\times {10}^{-5} {\mathrm{K}}^{-1}$, respectively. The value of $M$ is ______ $\mathrm{kg}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)