Question

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 ______$cm$.

Answer 1

$ \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 $