Q 11-09-044JEE MainJEE Main 2025 (22 Jan, Shift 2)Medium
A tube of length $1\ \text{m}$ is filled completely with an ideal liquid of mass $2M$, and closed at both ends. The tube is rotated uniformly in a horizontal plane about one of its ends. If the force exerted by the liquid at the other end is $F$, then angular velocity of the tube is $\sqrt{\dfrac{F}{\alpha M}}$ in SI unit. The value of $\alpha$ is ______.
Numerical value type. Enter your answer.
Answer: 1
The force from the far end wall supplies the centripetal force for the whole liquid column. Its centre of mass is at $L/2$ from the axis:
$$F = (2M)\,\omega^2\,\frac{L}{2} = M\omega^2L$$
With $L = 1\ \text{m}$: $F = M\omega^2 \Rightarrow \omega = \sqrt{\dfrac{F}{M}}$, so $\alpha = 1$.
Solution by Sreeraj P, M.Sc Physics