Q 11-08-069JEE MainJEE Main 2022 (25 Jul, Shift 1)Easy
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 $5\ \text{cm}$. Another wire of the same material of length $4L$ and radius $4r$ is pulled by a force $4F$ under the same conditions. The increase in length of this wire is ______ cm.
Numerical value type. Enter your answer.
Answer: 5
$\Delta l = \dfrac{FL}{\pi r^2Y}$:
$$\Delta l' = \frac{(4F)(4L)}{\pi(4r)^2Y} = \frac{16}{16}\Delta l = 5\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics