A metallic rod of Young's modulus 2 × 10¹¹ N m⁻² undergoes a strain of 0.5%. The energy stored per unit volume in the rod will be N × 10⁶ J m⁻³. Find N.
Physics · Mixed Chapter
JEE Main Practice

Question

A metallic rod of Young's modulus 2 × 10¹¹ N m⁻² undergoes a strain of 0.5%. The energy stored per unit volume in the rod will be N × 10⁶ J m⁻³. Find N.

G1 Physics · Accepted Answer

Step 1: Y = 2 × 10¹¹ Pa; ε = 0.5% = 0.005 = 5 × 10⁻³. Step 2: Elastic strain-energy density u = ½Yε². Step 3: u = ½ × 2 × 10¹¹ × (5 × 10⁻³)². Step 4: u = 10¹¹ × 25 × 10⁻⁶ = 2.5 × 10⁶ J m⁻³. Final answer: N = 2.5.