# Two separate wires A and B are stretched

Question:

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

Solution:

$(32)$

For $\mathrm{A} \frac{\mathrm{E}}{\pi \mathrm{r}^{2}}=\mathrm{y} \frac{2 \mathrm{~mm}}{\mathrm{a}} \ldots$ (1)

For $\mathrm{B} \frac{\mathrm{E}}{\pi \cdot 16 \mathrm{r}^{2}}=\mathrm{y} \frac{4 \mathrm{~mm}}{\mathrm{~b}} \ldots(2)$

$\therefore(1) /(2)$

$16=\frac{2 b}{4 a}$

$\frac{a}{b}=\frac{1}{32}$

$\therefore$ Answer $=32$