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JEE Main 2023 (15 Apr, Shift 1) · Young's Modulus & Elongation

Young's Modulus & Elongation question from JEE Main 2023 (15 Apr, Shift 1)

Q12JEE Main 2023 · 15 APR · SHIFT 1Easy

Young's Modulus & Elongation

A wire of length ' $L$ ' and radius ' $r$ ' is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$ , its length increases by ' $l$ '. Another wire of same material of length ' $2L$ ' and radius ' $2r$ ' is pulled by a force ' $2f$ '. Then the increase in its length will be:

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Answer: (c)

Same material: $\Delta L \propto \frac{fL}{r^2}$
$\frac{\Delta L'}{l} = \frac{2f \times 2L}{(2r)^2} \cdot \frac{r^2}{fL} = 1$
So the answer is (c) $l$ .

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