JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Elasticity & SHM

A steel wire of length 2 m and Young's modulus

2.0 \times 1 0^{11} Nm^{- 2}

is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and

1 0^{- 3}

respectively, then the elastic potential energy density of the wire is _______

\times 1 0^{5}

(in SI units)

Answer: 25

Solution

Poisson's ratio links the two strains, so the longitudinal strain is

ε = \frac{transverse strain}{μ} = \frac{1 0 ^{- 3}}{0.2} = 5 \times 1 0^{- 3}

. The elastic energy stored per unit volume is

u = \frac{1}{2} Y ε^{2} = \frac{1}{2} \times 2 \times 1 0^{11} \times (5 \times 1 0^{- 3})^{2} = 25 \times 1 0^{5}

SI units, so the required value is 25.

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Integer answer