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JEE Main 2009 (AIEEE) · Young's Modulus & Elongation

Young's Modulus & Elongation question from JEE Main 2009 (AIEEE)

Q31JEE Main 2009 · AIEEEMedium

Young's Modulus & Elongation

Two wires are made of the same material and have the same volume. However wire $1$ has cross- sectional area $A$ and wire $2$ has cross-sectional area $3A.$ If the length of wire $1$ increases by $\Delta x$ on applying force $F,$ how much force is needed to stretch wire $2$ by the same amount?

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Answer: (c)

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

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