Q 11-08-041JEE MainJEE Main 2024 (29 Jan, Shift 2)Easy
A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:
Answer: (D) 2 times
$$l = \frac{FL}{\pi r^2 Y} \;\Rightarrow\; l \propto \frac{F}{r^2}$$
$$\frac{l'}{l} = \frac{1/2}{(1/2)^2} = 2$$
The extension becomes 2 times.
Solution by Sreeraj P, M.Sc Physics