Q 11-13-028JEE MainMedium
A liquid column of total length $L$ in a U-tube of uniform cross-section is disturbed slightly and oscillates. Its period is
Answer: (B) $2\pi\sqrt{\dfrac{L}{2g}}$
If one side rises by $y$, the level difference is $2y$ and the restoring force is $2y\rho gA$. The moving mass is $\rho AL$:
$$\rho AL\,\ddot{y} = -2\rho gA\,y \;\Rightarrow\; \omega^2 = \frac{2g}{L} \;\Rightarrow\; T = 2\pi\sqrt{\frac{L}{2g}}$$
Solution by Sreeraj P, M.Sc Physics