Properties Of Matter

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 \(\mathrm{g=10~m~s^{-2}}\))