A metal rod of cross-sectional area $3 \times 10^{-6}\,\text{m}^2$ is suspended vertically from one end has a length $0.4\,\text{m}$ at $100^\circ\text{C}$. Now the rod is cooled up to $0^\circ\text{C}$, but prevented from contracting by attaching a mass $m$ at the lower end. The value of $m$ is ($Y = 10^{11}\,\text{N/m}^2$, coefficient of linear expansion $= 10^{-5}/\text{K}$, $g = 10\,\text{m/s}^2$)