Properties of Solids and Liquids: JEE Main 2023 Physics question

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 $210^{\circ} \mathrm{C}$ to $160^{\circ} \mathrm{C}$. After cooling, a mass $\mathrm{M}$ 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 $\mathrm{M}$ is __________ $\mathrm{kg}$. (Take $\mathrm{g=10~m~s^{-2}}$)