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. Them:
Text Solution
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Force applied on the body will be equal to upthrust for vertical oscillations.,
Let block is displaced through x m, then weight of displaced water or upthrust (upwards)
= – Ax ρ g
where A is area of cross-section of the block and ρ is its density. This must be equal to force (= ma)
applied, where m is mass of the block and a is acceleration.
∴ ma = – Ax ρ g or a = – 
x = – ω 2 x
This is the equation of simple harmonic motion.
Time period of oscillation
T = 
⇒ 
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