A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is $l$ . If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

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$l$

$\frac{l}{4}$ $2 l$

$\frac{l}{2}$

answer is D.

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Detailed Solution

$l = \frac{FL}{{πr}^{2} Y}$

$\Rightarrow \frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}} \frac{L_{2}}{L_{1}} {(\frac{r_{1}}{r_{2}})}^{2} = 2 \times 2 \times {(\frac{1}{2})}^{2} = 1$

$∴ l_{2} = l_{1}$

i.e. the increment in length will be same

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