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A rectangular block of mass of 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 with a time period T. then

(a) T ∝ 1/√m

(b) T  ∝ √ρ

(c) T∝ 1/√A

(d) T ∝1/ρ

1 Answer

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Best answer

Correct option  (c) T∝ 1/√A

Explanation:

Let I be the length of block immersed in liquid as shown in the figure. When the block rs floating,

If the block is given vertical displacement y then the effective restoring force is

Restoring force =-[Alρg]y.As this F is directed towards its equilibrium position of block, so if the block is left free, it will execute simple harmonic motion-

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