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
JEE MAIN 2021, Medium
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For $A \frac{ E }{\pi r ^{2}}= y \frac{2 mm }{ a }$ $......(1)$
For B $\frac{ E }{\pi \cdot 16 r ^{2}}= y \frac{4 mm }{ b }$ $..........(2)$
$\therefore(1) /(2)$
$16=\frac{2 b }{4 a }$
$\frac{ a }{ b }=\frac{1}{32}$
$=32$
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