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 \(....cm\).

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Correct Answer

(D) \(5\)

Step-by-step Solution

Detailed explanation

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

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

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