A thin uniform metallic rod, of length $$\ell = 1.0\,\text{m}$$ and area of cross section $$A = 2\,\text{mm}^2$$, is made to rotate with angular velocity $$\omega = 400\,\text{rad s}^{-1}$$ in a horizontal plane about a vertical axis through one of its ends. The density and the Young's modulus of the material of the rod are $$\rho = 10^4\,\text{kg m}^{-3}$$ and $$Y = 2.0\times10^{11}\,\text{N m}^{-2}$$. Taking $$r$$ as the distance of a point on the rod from the axis of rotation, the