A wire of length L and radius r is clamped rigidly at one end. When other end of wire is pulled by a

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8.Mechanical Properties of Solids

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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 $5\,cm$. Another wire of the same material of length $4 L$ and radius $4\,r$ is pulled by a force $4\,F$ under same conditions. The increase in length of this wire is $....cm$.

A

$2$

B

$3$

C

$4$

D

$5$

(JEE MAIN-2022)

Solution

$\Delta \ell_{1}=\frac{ F \ell}{ AY }=\frac{ F \ell}{\pi r ^{2} Y }=5\,cm$

$\Delta \ell_{2}=\frac{4 F 4 \ell}{\pi 16 r ^{2} Y }=\frac{ F \ell}{\pi r ^{2} Y }=5\,cm$

Standard 11

Physics

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