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A rectangular block of mass m and area of cross - section A floats in a liquid density ρ. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T, the T2 is proportional to

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In equilibrium position, let l be the length of the block immersed in the liquid as shown in figure.

Then, mg = Alρ

Or m = Alρ

If the block is given a further downward displacement y, then effective upward force (i.e. restoring force) on block is

it means F  y and it is directed towards equilibrium position. Therefore, if the block is left free, it will executes SHM mass of block = m = inertia factor spring factor = Aρg

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