Physics Question from JEE Main 2023 · 31 January, Shift 1

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