Question

A metallic wire is stretched by suspending a weight to it. If β is the stress produced in the wire and Y its Young’s modulus of elasticity, the potential energy stored per unit volume in the wire is

• A. β²Y/2
• B. βY/2
• C. β/2Y
• D. β²/2Y

Answer 1

Answer: (D)

β²/2Y

Answer 2

Elastic energy per unit volume = (1/2)stress × strain, Here, Strain = β

And Y = $\frac{Stress}{Strain}$ ∴ Strain = stress/Y = β/Y

∴ Strain = Y/ β

Elastic energy per unit volume = $\frac{\beta}{2} \times \frac{\beta}{Y} = \frac{\beta^{2}}{2Y}$