Question

A metal rod of Young's modulus $2\times {10}^{10}N{m}^{-2}$ undergoes an elastic strain of 0.02%. The energy per unit volume stored in the rod, in $Joules$ is ?

• A. $400$
• B. $800$
• C. $1200$
• D. $1600$

Answer 1

The correct option is A $400$

$\text{Energy per unit voume = Energy density}$

$\begin{array}{c}=\frac{1}{2}\times \text{stress}\times \text{strain}\\ =\frac{1}{2}\times \frac{F}{A}\times \frac{\Delta l}{l}\\ =\frac{1}{2}\times \left(\frac{\gamma }{l}\right)\left(\frac{\Delta l}{l}\right)\\ =\frac{1}{2}Y{\left(\frac{\Delta l}{l}\right)}^2\\ =\frac{1}{2}\times 2\times {10}^{10}\times {\left(\frac{0.02}{100}\right)}^2\end{array}$

$=400Joule$

$\text{Ans: (A)}$