Question 62 of 118

A uniform metallic wire is elongated by $0.04m$ when subjected to a linear force $F.$ The elongation, if its length and diameter is doubled and subjected to the same force will be _________ $cm.$

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Answer: 2

$F=Y.A\cdot \dfrac{\Delta l}{l}$$\Rightarrow \Delta l=\dfrac{F}{Y.A.}\cdot l$$\Rightarrow \Delta l=\dfrac{F.l}{Y.\pi {r}^{2}}$$\Rightarrow \Delta l\propto \dfrac{l}{{r}^{2}}$
$\dfrac{\Delta {l}_{2}}{\Delta {l}_{1}}=\left(\dfrac{{l}_{2}}{{l}_{1}}\right){\left(\dfrac{{r}_{1}}{{r}_{2}}\right)}^{2}$$=\left(2\right){\left(\dfrac{1}{2}\right)}^{2}$$\Rightarrow \dfrac{\Delta {l}_{2}}{\Delta {l}_{1}}=\dfrac{1}{2}$$\Rightarrow \Delta {l}_{2}=\dfrac{\Delta {l}_{1}}{2}$
$=\dfrac{0.04}{2}$$=0.02m$$\Rightarrow \Delta {l}_{2}=2cm$.

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