A thin rod having a length of 1 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 M is attached at the lower end of the rod such that the length of rod again becomes 1 m . Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} \mathrm{Nm}^{-2}$ and $2 \times 10^{-5} \mathrm{~K}^{-1}$, respectively. The value of M is $\_\_\_\_$ kg. (Take $\left.\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$