Question

A wire of length L and cross-sectional area A is constructed of a material whose Young's modulus of elasticity is Y. The energy density stored in the wire when stretched by $x$ meter will be

• A. $Y\times x^2$
• B. $\frac{Y\times x^2}{L}$
• C. $\frac{Y\times x^2}{2L^2}$
• D. $\frac{Y\times x^2}{L^2}$

Answer 1

The correct option is C $\frac{Y\times x^2}{2L^2}$

$EnergyDensity=\frac{1}{2}\times Stress\times Strain=\frac{1}{2}\times \frac{xY}{l}\times \frac{x}{l}(\because Stress=Y\times Strain)or,\frac{x^{2}Y}{2L^2}$