A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$ its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then find the increase in length of this wire.
A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$ its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then find the increase in length of this wire.
$\mathrm{Y}=\frac{\mathrm{FL}}{\mathrm{Al}}=\frac{f \mathrm{~L}}{\pi r^{2} l}$
$\therefore l=\frac{f \mathrm{~L}}{\pi r^{2} \mathrm{Y}}$
Now for increase in length for second wire,
$l^{\prime}=\frac{(2 f)(2 \mathrm{~L})}{\pi(2 r)^{2} l}$
$=\frac{4 f L}{4 \pi r^{2} l}$
$l^{\prime}=l$
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