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Q.

A force $F$ is applied on the wire of radius $r$ and length $L$ and change in the length of wire is $l$ . If the same force $F$ is applied on the wire of the same material and radius $2 r$ and length $2 L$ , Then the change in length of the other wire is:

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a

$l$

b

$2 l$

c

$l / 2$

d

$4 l$

answer is C.

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Detailed Solution

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

i.e. the change in the length of other wire is $\frac{l}{2}$ .

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