Question

A uniform metal rod of 2 mm² cross section is heated from 0ºC to 20ºC. The coefficient of linear expansion of the rod is 12 × 10^–6/ºC, its Young's modulus is 10¹¹ N/m². The energy stored per unit volume of the rod is –

• A. 2880 J/m³
• B. 1500 J/m³
• C. 5760 J/m³
• D. 1440 J/m³

Answer 1

Answer: (A)

2880 J/m³

Answer 2

$\frac{Energy}{volume}$ = $\frac{1}{2}$ × stress × strain

=$\frac{1}{2}$×(YaDT) × $\left( \frac{\Delta\mathcal{l}}{\mathcal{l}} \right)$ = $\frac{1}{2}$YaDT× $\left( \frac{\mathcal{l} \propto \Delta T}{\mathcal{l}} \right)$

= $\frac{1}{2}$ Y a²(DT)² = 2880 J/m³