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A cylindrical block of mass M and cross-sectional area A floats with its axis vertical in a liquid of density ρ. Depressed a little and released, it oscillates. The period of oscillation is

Asked in JEE Main 24th Jan 1st Shift 2026 · Floating bodies and gas columns

Answer: (4) 2π√M/(ρ Ag)

Step-by-step solution

Pushing the block down by x displaces an extra volume Ax of liquid, so the restoring force is F=-ρ Agx and the effective force constant is k=ρ Ag.

T=2π√M/k=2π√M/(ρ Ag).

Why the other options are wrong

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