Q 11-04-067JEE MainJEE Main 2025 (24 Jan, Shift 2)Medium
A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The mass makes $\left(\dfrac{3}{\pi}\right)$ rotations per second about the vertical axis passing through the end of the string as shown. The tension in the string is ______ $ML$.
Numerical value type. Enter your answer.
Answer: 36
This is a conical pendulum. The mass moves in a circle of radius $R = L\sin\theta$. The horizontal component of tension supplies the centripetal force:
$$T\sin\theta = M\omega^2(L\sin\theta) \Rightarrow T = M\omega^2L$$
$\omega = 2\pi f = 2\pi\times\dfrac{3}{\pi} = 6\ \text{rad/s}$, so $T = 36\,ML$.
Solution by Sreeraj P, M.Sc Physics