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 $2r$ and length $2L$, 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, $l=\frac{FL}{Ay}$
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 $\frac{l}{2}$.