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JEE Main 2024 (29 Jan, Shift 2) · Young's Modulus & Elongation

Young's Modulus & Elongation question from JEE Main 2024 (29 Jan, Shift 2)

Q7JEE Main 2024 · 29 JAN · SHIFT 2Easy

Young's Modulus & Elongation

A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$ , its length increases by $l$ . If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

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Answer: (a)

$\Delta L \propto \frac{F}{r^2}$ for the same $L$ and material.
$\frac{\Delta L'}{l} = \frac{F/2}{(r/2)^2} \cdot \frac{r^2}{F} = \frac{1/2}{1/4} = 2$
So the answer is (a) 2 times.

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