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NEET 2018 · Young's Modulus & Elongation

Young's Modulus & Elongation question from NEET 2018

Q27NEET 2018Medium

Young's Modulus & Elongation

Two wires are made of the same material and have the same volume. The first wire has cross- sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by $\Delta$ l on applying a force F, how much force is needed to stretch the second wire by the same amount?

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Answer: (c)

Same volume: $L = \frac{V}{A}$ , so $F = \frac{YA\Delta l}{L} = \frac{YA^2 \Delta l}{V} \propto A^2$ for the same $\Delta l$ .
$\frac{F_2}{F_1} = \left(\frac{3A}{A}\right)^2 = 9$
So the answer is (c) $9F$ .

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