A cylindrical block of mass M and area of cross section A is floating in a liquid of density and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is

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Quantrex Academy · Accepted Answer

Correct answer: D. 2 π (M)/( A g)

When the block is depressed by distance

x

, the additional buoyant force is

F = \rho Agx

acting upward as restoring force.
Equation of motion:

M\frac{d^2x}{dt^2} = -\rho Agx

.
This gives

\omega^2 = \frac{\rho Ag}{M}

.
Period of oscillation:

T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{M}{\rho Ag}}

A cylindrical block of mass M and area of cross section A is...

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