Two separate wires A and B are stretched by 2 ,mm and 4, mm respectively, when they are subjected to

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8.Mechanical Properties of Solids

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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

A

$24$

B

$36$

C

$42$

D

$32$

(JEE MAIN-2021)

Solution

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

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

$\therefore(1) /(2)$

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

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

$=32$

Standard 11

Physics

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