Question

A uniform iron rod of length $L$ and radius $r$ is suspended from the ceiling by one of its end . What will be the elastic potential energy stored in the rod due to its own weight , given ${\rho }^2{g}^2{L}^{3}A=12Y$ where $\rho$ and Y are the density and young's modulus of the iron rod respectively ? $[A=\pi r^2]$

Answer 1

$E=\frac{M^2{g}^{2}L}{6AY}$

$=\frac{{(\rho \cdot AL)}^2\cdot g^2\cdot L}{6AY}$

$=\frac{{\rho }^2{A}^2{L}^2\cdot g^{2}L}{6AY}$

$=\frac{1}{6}\frac{{\rho }^2{g}^2{L}^{3}A}{Y}$