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Question

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

A
Tρ
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B
Tρ0
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C
T1ρ
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D
T1ρ
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Solution

The correct option is D T1ρ
For a block of mass m and cross-sectional area A floating in a liquid of density ρ, if it is given a very small vertical push it will start to perform simple harmonic motion due to restoring force provided by buoyancy.

The time period of oscillation is given by,
T=2πmρAg
where m=σ×V, is the mass of block and σ be the density of block.

Hence time period of oscillation of block is inversely proportional to square root of density of liquid.
T1ρ

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