Question

A Young's modulus of the material of a wire is $2\times {10}^{10}N{m}^{-2}.$ If the elongation strain is $1$ the energy stored in the wire per unit volume in $J{m}^{-3}$ is

• A. ${10}^{6}J{m}^{-3}$
• B. ${10}^{8}J{m}^{-3}$
• C. $2\times {10}^{6}J{m}^{-3}$
• D. $2\times {10}^{8}J{m}^{-3}$

Answer 1

The correct option is A ${10}^{6}J{m}^{-3}$

$\begin{array}{c}\text{Given}\\ \text{Strain}=\frac{\Delta L}{L}=\frac{1}{100}\end{array}$

$\text{young's modulus of wire}=2\times {10}^{10}N/m^2$

$\begin{array}{c}\text{we know;}\\ \text{Energy stored per unit volume}=\frac{1}{2}\times \text{stress}\times \text{strain}\\ y=\frac{\text{stress}}{\text{strain}}\end{array}$

$E=\frac{1}{2}\times (\text{strain}{)}^2\times y$

$\begin{array}{cc}& =\frac{1}{2}\times {\left(\frac{1}{100}\right)}^2\times 2\times {10}^{10}\\ E& ={10}^{6}J\end{array}$