Question

When an elastic material with Young's modulus ${}^{\prime }{Y}^{\prime }$ is subjected to a stretching stress ${}^{\prime }{S}^{\prime }$, then the elastic energy stored per unit volume is:

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

Answer 1

Answer: (A)

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

Elastic energy stored per unit volume $=\frac{1}{2}\times stress\times strain$
$=\frac{1}{2}S\times \left(\frac{S}{Y}\right)$
$=\frac{S^2}{2Y}$