# A brass rod of 2m is stretched by 1cm have crosssectional area $2cm^2$ .If a force of $10^5$N is applied on it.What is elastic potential energy density?

$\begin{array}{1 1}(A)\;6.2mJ\\(B)\;3.1mJ\\(C)\;1.5mJ\\(D)\;\text{None}\end{array}$

Energy density =$\large\frac{1}{2}$$\times stress\timesstrain \Rightarrow \large\frac{1}{2}\times \frac{f}{a}\times \frac{\Delta l}{l} \Rightarrow \large\frac{1}{2}\times \frac{10^5}{2\times 10^{-4}}\times \frac{10^{-2}}{2} \Rightarrow \large\frac{1}{8}$$\times 10^{-1}$
$\Rightarrow 3.125\times 10^{-3}J$
$\Rightarrow 3.125mJ$
Hence (B) is the correct answer.