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