A steel wire of length 2 m and Young's modulus 2.0 × 10¹¹ N m⁻² is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and 10⁻³ respectively, then the elastic potential energy density of the wire is __________ × 10⁵ (in SI units). Numerical answer type. Work it out, then open the answer.

Answer: 25. Longitudinal strain = (transverse strain)/(σ) = 10⁻³0.2 = 5 × 10⁻³. u = 1/2Yε² = 1/2 × 2 × 10¹¹ × 25 × 10⁻⁶ u = 25 × 10⁵ J/m³ So the answer is 25.

A steel wire of length 2 m and Young's modulus 2.0 × 10¹¹ N m⁻² is… | JEE Main 2025 (2 Apr, Shift 1)

Q2JEE Main 2025 · 2 APR · SHIFT 1Medium

Elastic Potential Energy

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11}\text{ N m}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is __________ $\times 10^{5}$ (in SI units).

Numerical answer type. Work it out, then open the answer.

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Answer: 25

Longitudinal strain $= \dfrac{\text{transverse strain}}{\sigma} = \dfrac{10^{-3}}{0.2} = 5 \times 10^{-3}$ .
$u = \dfrac{1}{2}Y\varepsilon^2 = \dfrac{1}{2} \times 2 \times 10^{11} \times 25 \times 10^{-6}$
$u = 25 \times 10^5\text{ J/m}^3$
So the answer is 25.

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