Question

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

• A. 16
• B. 8
• C. 4
• D. 1/4

Answer 1

Answer: (A)

16

Work done $=\frac{AY}{2L}{l}^2$$=\frac{\pi r^{2}Y{l}^2}{2L}$
Work done $\propto \frac{r^2}{L}$
$\frac{w_1}{w_2}=\frac{r{{}_1}^2}{L_1}\times \frac{1/2L_1}{(2r_1{)}^2}$
$\frac{w_1}{w_2}=\frac{1}{8}$
$w_2=8w_1$
$=8\left(2\right)$
$=16J$