Question

The Young's modulus of the material of a rod is $20\times {10}^{10}$ pascal. When the longitudinal strain is 0.04%, The energy stored per unit volume is

• A. $4\times {10}^{3}J/m^3$
• B. $8\times {10}^{-3}J/m^3$
• C. $16\times {10}^{-3}J/m^3$
• D. $16\times {10}^{3}J/m^3$

Answer 1

The correct option is D $16\times {10}^{3}J/m^3$

$\begin{array}{c}\text{Energy stored per unit volume}=\frac{1}{2}\times \text{stress}\times \text{strain.}\\ \begin{array}{c}\text{Giuen}y=20\times {10}^{10}Pa\text{and}\text{strain}=0.04\%\\ y=\frac{\text{Stress}}{\text{strain.}}\Rightarrow \text{stress}=y\left(\text{strain}\right)\end{array}\end{array}$

$\begin{array}{cc}\Rightarrow \text{Energy stored}& \text{Per unit volume}=\frac{1}{2}\times Y(\mathrm{strain}{)}^2\\ & =\frac{1}{2}\times 20\times {10}^{10}\times {(4\times {10}^{-4})}^2\\ & =10\times {10}^{10}\times 16\times {10}^{-8}\\ & =16\times {10}^{3}J/m^3\end{array}$