Q. In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain $\sigma\ $and modulus of elasticity Y is
A) $\frac{Y\sigma^{2}}{2}$
B) $\frac{Y\sigma}{2}$
C) $\frac{2Y\sigma^{2}}{2}$
D) $\frac{Y^{2}\sigma}{2}$
Explanation
(a) Energy density = $\frac{1}{2}\ \times stress\ \times strain\ $
$Y = \frac{stress}{\sigma}\ \ \ or\ \ stress = Y\sigma$
$\therefore\ \ energy\ density = \frac{1}{2}\ Y\sigma\ \times \sigma = \frac{Y\sigma^{2}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.