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
A$l$
B$2l$
C$\frac{l}{2}$
D$\frac{l}{4}$
AIIMS 1980, Medium
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A$l$
a (a) $l = \frac{{FL}}{{AY}} = \frac{{FL}}{{\pi {r^2}Y}}\therefore l \propto \frac{{FL}}{{{r^2}}}$ ($Y =$ constant)
${l_2} = {l_1}$ i.e. increment in its length will be $l.$
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