Question

If work done for stretching a wire by $1mm$ is $2J$, then the work necessary for stretching another wire of same material, but with double the radius and half the length by $1mm$ (in Joule) is

• A. $16$
• B. $8$
• C. $4$
• D. $1$

Answer 1

The correct option is A $16$

The work done in stretching a wire is defined as,
$W=\frac{AY{l}^2}{2L}=\frac{\pi r^{2}Y{l}^2}{2L}$
Here
$r$ is radius of the wire
$L$ is length of the wire
$l$ is extension of the wire
$Y$ is Youngs Modulus

$\Rightarrow W\propto \frac{r^2}{L}$
$\frac{W_1}{W_2}=\frac{r_1^2}{(r_2{)}^2}\times \frac{L_2}{L_1}$
$\frac{W_1}{W_2}=\frac{r_1^2}{(2r_1{)}^2}\times \frac{L_1/2}{L_1}$
$\frac{W_1}{W_2}=\frac{1}{8}$
$W_2=8W_1$

Given,
$W_1=2J$
$\Rightarrow W_2=16J$