Question

A metal rod of Young's modulus $2\times {10}^{10}newton/mete{r}^2$, undergoes an elastic strain of $0.06$ %. The energy per unit volume stored in $joule/metr{e}^3$

• A. $3600$
• B. $7200$
• C. $1800$
• D. $900$

Answer 1

The correct option is A $3600$

$\begin{array}{cc}& Y=2\times {10}^{10}N/m^2\\ & \frac{\Delta l}{l}=\frac{0.06}{100}\\ & \text{Energy per unit volume}=\frac{1}{2}\text{(stress) (strain)}\end{array}$

$\begin{array}{cc}& =\frac{1}{2}Y{\left(\frac{\Delta l}{l}\right)}^2\\ =& \frac{1}{2}\times 2\times {10}^{10}\times {\left(\frac{0\cdot 06}{100}\right)}^2\\ =& \frac{{10}^{10}\times 36\times {10}^{-4}}{100\times 100}\\ =& 3600J/m^3\end{array}$

$\text{Hence, answer is (A)}$