# Two steel wire are hang from roof.Their length and radius are in the ratio 3 : 5 and 1 : 2 respectively.If the extension in first wire is 2mm,what is extension in other if force applied is in the ratio 2 : 3?

$\begin{array}{1 1}(A)\;2mm\\(B)\;1.25mm\\(C)\;1mm\\(D)\;3.25mm\end{array}$

Given : $\large\frac{l_1}{l_2}=\frac{3}{5}$
$\large\frac{a_1}{a_2}=(\frac{r_1}{r_2})^2=(\frac{1}{2})^2=\frac{1}{4}$
$\large\frac{F_1}{F_2}=\frac{2}{3}$
$\Delta l_1$=2mm
As 2 wires are of same material their young modulus is same
$Y=(\large\frac{F}{a})\frac{l}{\Delta l}$
$\Rightarrow (\large\frac{F_1}{a_1})\frac{l_1}{\Delta l_1}=(\large\frac{F_2}{a_2})\frac{l_2}{\Delta l_2}$
$\Delta l_2=(\large\frac{F_2}{F_1})(\frac{a_1}{a_2})(\frac{l_2}{l_1})$$\Delta l_1 \Rightarrow \large\frac{3}{2}\times \frac{1}{4}\times \frac{5}{3}$$\times 2$mm
$\Rightarrow \large\frac{5}{4}$mm
$\Rightarrow$ 1.25mm
Hence (B) is the correct answer.