Question

A uniform wire of Youngs modulus Y is stretched by a force within the elastic limit. If S is the stress produced in the wire and $\epsilon$ is the strain in it, the potential energy stored per unit volume is given by

• A. $\frac{1}{2}\epsilon S$
• B. $\frac{1}{2}Y{\epsilon }^2$
• C. $\frac{S^2}{2Y}$
• D. $\frac{1}{2}Y\epsilon S$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\frac{1}{2}\epsilon S$
B $\frac{1}{2}Y{\epsilon }^2$
C $\frac{S^2}{2Y}$

$energy=\frac{1}{2}\times strain\times stress\times volume$
$\frac{energy}{volume}=\frac{1}{2}\times strain\times stress$
$=\frac{1}{2}S\epsilon$
$=\frac{1}{2}\times Y\times strain\times strain(\therefore Y=\frac{stress}{strain})$
$=\frac{1}{2}Y{\epsilon }^2$
$=\frac{1}{2}\times stress\times \frac{stress}{Y}$
$=\frac{1}{2}\frac{S^2}{Y}$