Question

Young's modulus of material of wire is '$Y$' and strain energy per unit volume is '$E$', then the strain is

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

Answer 1

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

Energy per unit volume $E=\frac{1}{2}\times Stress\times Strain$ ........(1)

But from Hooke;s law, $Stress=Y\times Strain$

$\therefore$ Equation (1) becomes $E=\frac{1}{2}Y\times (Strain{)}^2$

$⟹$ $Strain=\sqrt{\frac{2E}{Y}}$