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

Answer 1

Answer: 5

$\Delta {\ell }_1=\frac{F\ell }{AY}=\frac{F\ell }{\pi r^{2}Y}=5cm$
$\Delta {\ell }_2=\frac{4F4\ell }{\pi 16r^{2}Y}=\frac{F\ell }{\pi r^{2}Y}=5cm$