Q. The elastic energy stored in a wire of Young’s modulus Y is
A) $\frac{1}{2}Y \times stress \times strain \times volume$
B) $\frac{{(stress)}^{2} \times volume}{2Y}$
C) $stress \times strain \times volume$
D) $Y \times \frac{{(stress)}^{2}}{volume}$
Explanation
(b) When a wire is stretched work is done against the interatomic forces. This work is stored in the wire in the form of elastic potential energy.
$W = \frac{1}{2} \times stress \times strain \times volume\ of\ wire$
Also, when strain in small, ratio of longitudinal stress to corresponding longitudinal strain is called Young’s modulus of material of body.
$Y = \frac{longitudinal\ stress}{longitudinal\ strain}$
$\therefore W = \frac{1}{2} \times stress \times \frac{stress}{Y} \times volume$
$= \frac{{(stress)}^{2} \times volume}{2Y}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.