Question

A force $F$ is applied on the wire of radius $r$ and length $L$ and change in the length of wire is $l$. If the same force $F$ is applied on the wire of the same material and radius $2\, r$ and length $2\, L$, then the change in length of the other wire is

• A. $l$
• B. $2l$
• C. $\frac{l}{2}$
• D. $4l$

Answer 1

Answer: (C)

Elongation, $l=\frac{F L}{A y}$
or $l \propto \frac{L}{r^{2}}$
$\therefore \frac{l_{2}}{l_{1}} =\frac{L_{2}}{L_{1}} \times\left(\frac{r_{1}}{r_{2}}\right)^{2}$
$=2 \times\left(\frac{1}{2}\right)^{2} =\frac{1}{2}$
or $l_{2} =\frac{l_{1}}{2}$
The change in the length of other wire is $\frac{l}{2}$.