A thin rod having a length of 1 m and area of cross-section 3 × 10^-6 m^2 is suspended vertically from one end. The rod is cooled from 210^° C to…

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