Q 11-13-046JEE MainJEE Main 2026 (24 Jan, Shift 1)Easy
A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ______
Answer: (C) $2\pi\sqrt{\dfrac{M}{\rho Ag}}$
Pushing the block down by $y$ adds buoyant force $\rho Ayg$, which acts upward (restoring):
$$M\frac{d^2y}{dt^2} = -\rho Ag\,y\Rightarrow\omega^2 = \frac{\rho Ag}{M}$$
$$T = 2\pi\sqrt{\frac{M}{\rho Ag}}$$
Solution by Sreeraj P, M.Sc Physics