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When a uniform wire of radius $r$ is stretched by a $2 k g$ weight, the increase in its length is $2.00 m m$ . If the radius of the wire is $r / 2$ and other conditions remain the same, the increase in its length is:

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$2.00 m m$

$4.00 m m$

$6.00 m m$

$8.00 m m$

answer is D.

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Detailed Solution

$l = \frac{F L}{{πr}^{2} Y} ∴ l \propto \frac{1}{r^{2}} (F, L a n d Y a r e c o n s \tan t) \Rightarrow \frac{l_{2}}{l_{1}} = {(\frac{r_{1}}{r_{2}})}^{2} = {(2)}^{2} \Rightarrow l_{2} = 4 l_{1} = 4 \times 2 = 8 m m$

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