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) $2\pi\sqrt{\dfrac{L}{2g}}$
Concept. If one side rises by $y$, the level difference $2y$ gives a restoring force $2\rho gAy$ acting on the whole column mass $\rho AL$.
Step 1. Equation of motion.
$$\rho AL\ddot y = -2\rho gAy \;\Rightarrow\; \omega^2 = \frac{2g}{L}$$
Step 2. Period. $T = 2\pi\sqrt{\dfrac{L}{2g}}$.
Answer. $2\pi\sqrt{\dfrac{L}{2g}}$ (Option B).
Solution by Sreeraj P, M.Sc Physics