Question

The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$, then the strain will be

• A. $\sqrt{\frac{2E}{Y}}$
• B. $E\sqrt{2Y}$
• C. $\sqrt{\frac{E}{Y}}$
• D. $\frac{E}{Y}$

Answer 1

The correct option is A $\sqrt{\frac{2E}{Y}}$

$\begin{array}{c}\text{Given}\\ \text{young's modulus}=Y\\ \text{Energy per unit volume}=E\\ \text{we know,}\\ E=\frac{1}{2}\times \text{stress}\times \text{strain}\end{array}$

$\begin{array}{cc}y& =\frac{\text{stress}}{\text{strain}}\\ E=\frac{1}{2}\cdot y\cdot (\text{strain}{)}^2& \\ \text{strain}=& \sqrt{\frac{2E}{y}}\end{array}$