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

(A) $2 \pi \sqrt{\frac{M}{\rho A g}}$

(B) $\pi \sqrt{\frac{2 \mathrm{M}}{\rho \mathrm{Ag}}}$

(C) $\pi \sqrt{\frac{\rho \mathrm{A}}{\mathrm{Mg}}}$

(D) $2 \pi \sqrt{\frac{\rho \mathrm{~A}}{\mathrm{Mg}}}$

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Elasticity & SHM

A cylindrical block of mass M and area of cross section A is floating in a liquid of density

ρ

and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is

Answer: (A)

At equilibrium the weight is balanced by buoyancy,

ρ A h g = M g

. On depressing the block by a small distance

x

, the extra submerged volume provides a restoring force

F = - ρ A g x

, so the acceleration is

a = - \frac{ρ A g}{M} x

. This is simple harmonic with

ω^{2} = \frac{ρ A g}{M}

. The period of oscillation is

2 π \frac{M}{ρ A g}

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Single correct option