Question

A wire is stretched by a force $F$. If $s$ is the strain developed and $Y$ is Young's modulus of material of wire, then work done per unit volume is

• A. $\frac{Y{s}^2}{2}$
• B. $\frac{s^2}{2Y}$
• C. $\frac{1}{2}Fs$
• D. $\frac{Y}{2s^2}$

Answer 1

Answer: (A)

$\frac{Y{s}^2}{2}$

Work done per unit volume is same as energy per unit volume which is given by:
$\frac{1}{2}\times Stress\times Strain=1/2\times (Y\times Strain)\times Strain=\frac{1}{2}\times Y\times {\left(Strain\right)}^2=\frac{Y{s}^2}{2}$