The Young's modulus of the material of a rod is 20 × 10¹⁰ Pa. When the longitudinal strain is 0.04%, the energy stored per unit volume is N × 10³ J m⁻³. Find N.
Physics · Mixed Chapter
JEE Main Practice

Question

The Young's modulus of the material of a rod is 20 × 10¹⁰ Pa. When the longitudinal strain is 0.04%, the energy stored per unit volume is N × 10³ J m⁻³. Find N.

G1 Physics · Accepted Answer

Step 1: Young's modulus Y = 20 × 10¹⁰ = 2 × 10¹¹ Pa. Step 2: Strain ε = 0.04% = 0.04/100 = 4 × 10⁻⁴. Step 3: Elastic strain-energy density u = ½ × stress × strain = ½Yε². Step 4: u = ½ × 2 × 10¹¹ × (4 × 10⁻⁴)² = 10¹¹ × 16 × 10⁻⁸ = 16 × 10³ J m⁻³. Final answer: N = 16.