Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are…

Two separate wires A and B are stretched by $\displaystyle 2$ mm and $\displaystyle 4$ mm respectively, when they are subjected to a force of $\displaystyle 2$ N. Assume that both the wires are made up of same material and the radius of wire B is $\displaystyle 4$ times that of the radius of wire A. The length of the wires A and B are in the ratio of $\displaystyle \mathrm{a}: \mathrm{b}$. Then $\displaystyle \frac{\mathrm{a}}{\mathrm{b}}$ can be expressed as $\displaystyle \frac{1}{x}$ where $\displaystyle x$ is \_\_\_\_.