NEET (UG) 2024 — Question 30

The maximum elongation occurs when the stress equals the elastic limit. Use the formula for Young's modulus: $Y = \frac{\text{stress}}{\text{strain}} = \frac{\sigma}{\Delta L / L}$. Rearrange to find elongation: $\Delta L = \frac{\sigma L}{Y}$. Substitute the given values: $\sigma = 8 \times 10^8 \, \text{N m}^{-2}$, $L = 1 \, \text{m}$, $Y = 2 \times 10^{11} \, \text{N m}^{-2}$. Calculate: $\Delta L = \frac{(8 \times 10^8) \times 1}{2 \times 10^{11}} = 4 \times 10^{-3} \, \text{m}$. Convert to mm: $4 \times 10^{-3} \, \text{m} = 4 \, \text{mm}$. Thus, the maximum elongation is 4 mm, which corresponds to option A.