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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 $2 L$ and radius $2 r$ is stretched with a force of $2 F$ , the increase in its length will be:

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$l$

$2 l$

$\frac{l}{2}$

$\frac{l}{4}$

answer is A.

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Detailed Solution

$l = \frac{F L}{{πr}^{2} Y} \Rightarrow \frac{l_{2}}{l_{1}} = \frac{F_{2}}{F_{1}} \frac{L_{2}}{L_{1}} {(\frac{r_{1}}{r_{2}})}^{2} = 2 \times 2 \times \frac{1}{2} = 1 ∴ l_{2} = l_{1}$

i.e. the increment in length will be same.

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