Question:

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

Updated On: Jul 2, 2022
  • $l$
  • $2l$
  • $\frac{l}{2}$
  • $4l$
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The Correct Option is C

Solution and Explanation

Elongation, $l=\frac{F L}{A y}$ or $l \propto \frac{L}{r^{2}}$ $\therefore \frac{l_{2}}{l_{1}} =\frac{L_{2}}{L_{1}} \times\left(\frac{r_{1}}{r_{2}}\right)^{2}$ $=2 \times\left(\frac{1}{2}\right)^{2} =\frac{1}{2}$ or $l_{2} =\frac{l_{1}}{2}$ The change in the length of other wire is $\frac{l}{2}$.
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