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

The correct answer is 5
$\Delta l_1=\frac{Fl}{AY}=\frac{Fl}{\pi r^2Y}$ = 5cm
$\Delta l_2=\frac{4F4l}{\pi 16r^2Y}=\frac{Fl}{\pi r^2Y}$ = 5cm