Linear mass density of the given vertical rod varies as  $\lambda ={\lambda }_{0}x$, where  ${\lambda }_0=900kg/m^2$ and x is distance from upper end. Young’s modulus and cross sectional area of the rod is  $Y=1.8\times {10}^{11}N/m^2$ and  $A=2\times {10}^{-3}{m}^2$. If length of wire is 10m then calculate elongation of rod due to its own weight (in cm)  $g=10m/{\sec }^2$