The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are $8\times {10}^{8}\mathrm{N}{\mathrm{m}}^{-2}$ and $2\times {10}^{11}\mathrm{N}{\mathrm{m}}^{-2}$, is :

[NEET 2024]

Question

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are $8\times {10}^{8}\mathrm{N}{\mathrm{m}}^{-2}$ and $2\times {10}^{11}\mathrm{N}{\mathrm{m}}^{-2}$, is :

[NEET 2024]

YESPYQ · Accepted Answer

Correct answer: a) 4 mm. Under the elastic limit , the maximum permissible stress = $8\times {10}^{8}\text{ }\mathrm{N}\mathrm{/}{\mathrm{m}}^{2}$. Since $\text{strain}\text{ }=\text{ }\frac{\text{stress}}{Y},\ \Delta L\text{ }=\text{ }\text{(strain)}\times L,$ we get ${\mathrm{ΔL}}_{\max }=(\frac{8\times {10}^{8}}{2\times {10}^{11}})\times 1\text{ }\mathrm{m}=4\times {10}^{−3}\text{ }\mathrm{m}=4\text{ }\mathrm{m}\mathrm{m}\mathrm{.}$

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively…

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