Question

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 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 $1 / x$ where $x$ is________.

Answer 1

For A $\frac{ E }{\pi r ^{2}}= y \frac{2\,mm }{ a }\,\,\,\,\, ......(1)$
For $B \frac{ E }{\pi \cdot 16 r ^{2}}= y \frac{4\,mm }{ b }\,\,\,\,.......(2)$
$\therefore (1)\,\,(2)$
$16=\frac{2 b }{4 a }$
$\frac{a}{b}=\frac{1}{32}$
$\therefore $ Answer $=32$