Question

If in a wire of Young’s modulus $ Y $ , longitudinal strain $ X $ is produced then the potential energy stored in its unit volume will be

• A. $ 0.5 \,Y \,X ^2 $
• B. $ 0.5 \,Y^2 X $
• C. $ 2\,Y\,X^2 $
• D. $ Y\,X^2 $

Answer 1

Answer: (A)

Elastic potential energy per unit volume
$ U=\frac{1}{2}\times \text{stress}\times \text{strain} $
From definition of Young's modulus of wire
$ Y=\frac{\text{stress}}{\text{strain}} $
$ \Rightarrow $ Stress $=Y\times$ strain
Given, strain=X
= $ U=\frac{1}{2}TX^2 $
$ \Rightarrow U=0.5YX^2 $