A metal wire is stretched by suspending weight to it. If X is the longitudinal strain and Y is the Young’s modulus of elasticity, then the elastic potential energy per unit volume is

Engineering

Physics

Acceleration

Equilibrium

Stress Strain and Hookes Law New

Question

A metal wire is stretched by suspending weight to it. If X is the longitudinal strain and Y is the Young’s modulus of elasticity, then the elastic potential energy per unit volume is

$X^{2} / 2 Y$

$X^{2} / 2 Y^{2}$

$Y^{2} / 2 X$

$\frac{1}{2} {YX}^{2}$

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Elastic potential energy per unit volume (U) is the energy stored due to deformation. For a wire under tension, it is given by U = (1/2) × Stress × Strain. Stress is related to strain by Young's modulus Y: Stress = Y × Strain (X). Substituting, U = (1/2) × (Y × X) × X = (1/2) Y X².

Final answer: $\frac{1}{2} {Y X}^{2}$