Question

Two wires A and B of the same material have their lengths in the ratio of 1:2 and their diameters in the ratio of 2:1. If they are stretched with the same force, the ratio of the increase in the length of A to that of B will be

• A. 1:2
• B. 4:1
• C. 1:8
• D. 1:4

Answer 1

The correct option is C

1:8

Here, $l_1=\frac{F{L}_1}{\pi r_1^{2}Y}$ and $l_2=\frac{F{L}_2}{\pi r_2^{2}Y}$.
Therefore, $\frac{l_1}{l_2}=\frac{L_1}{L_2}\times {\left(\frac{r_2}{r_1}\right)}^2$
Given that, $L_2=2L_1$ and $r_2=\frac{r_1}{2}$
Thus, $\frac{l_1}{l_2}=\frac{1}{2}\times \frac{1}{(2{)}^2}=\frac{1}{8}$.
Hence, the correct choice is (c).