Question

If the elastic deformation energy of a steel rod of mass $m=3.1kg$ stretched to a tensile strain $\epsilon =1.0\times {10}^{-3}$ is $x$,then value of $100x$ is:

Answer 1

We assume that the deformation is wholly due to external load, neglecting the effect of the weight of the rod. Then a well known formula says, elastic energy per unit volume
$=\frac{1}{2}stress\times strain=\frac{1}{2}\sigma \epsilon$
This gives $\frac{1}{2}\frac{m}{\rho }E{\epsilon }^2\approx 0.04kJ$ for the total deformation energy.