A uniform rod of mass m and length l is rotating with constant angular velocity $\mathrm{\omega }$ about an axis which passes through its one end is perpendicular to the length of rod. The area of cross section of the rod is A and its Young’s modulus is Y. neglect gravity. Elongation of the entire rod is $\frac{{\mathrm{\rho \omega }}^2{\mathrm{L}}^3}{\mathrm{\eta Y}}$. Find the value of $\mathrm{\eta }$.