An aluminium rod with Young's modulus Y = 7.0 × 10¹⁰ N m⁻² undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is:
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Question

An aluminium rod with Young's modulus Y = 7.0 × 10¹⁰ N m⁻² undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is:

G1 Physics · Accepted Answer

Elastic energy stored per unit volume is u = (1/2)(stress)(strain) Using stress = Y×strain: u = (1/2)Y(strain)² Given: Y = 7.0×10¹⁰ N m⁻² strain = 0.04% = 4×10⁻⁴ Therefore, u = (1/2)(7.0×10¹⁰)(4×10⁻⁴)² = 3.5×10¹⁰ × 16×10⁻⁸ = 5.6×10³ J m⁻³ = 5600 J m⁻³ Hence option A follows.