A wire is stretched by 0.01m by a certain force 'F' another wire of same material whose diameter and lengths are double to original wire is stretched by the same force then its elongation will be ....

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0.005m

0.02m

0.04m

0.01m

answer is A.

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Detailed Solution

e₁ = 0.01m = 10^-2 m F₁ = F₂ = F
Let $r_{1} = \frac{D}{2}, r_{2} = \frac{2 D}{2} = D$
l₁ = l l₂ = l e₂ = ?
$e \propto \frac{I}{r^{2}}$

$\Rightarrow e_{2} = \frac{l_{2}}{l_{1}} x \frac{{r_{1}}^{2}}{{r_{2}}^{2}} x e_{1} = 0.005 m$

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