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 $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be
JEE MAIN 2023, Medium
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$\frac{2 f }{\pi(2 r )^2}= Y \frac{\ell^{\prime}}{2 L }$
$\Rightarrow \frac{2}{1}=\frac{2 \ell^{\prime}}{\ell} \Rightarrow \ell^{\prime}=\ell$
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