Question

20. A rectangular block of mass m and area of
cross-section A floats in a liquid of density ñ. If it is
given a small vertical displacement from equilibrium
it undergoes oscillation with a time period T. Then
[AIPMT (Prelims)-2006]
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Answer 1

Answer: T∝ 1/√A

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explanation:-

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

mg=Alpm

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

F= -Alpgy

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-

Spring factor:-Aρg

therefore, time period = T = 2π√m/apg

thats means T directly proportional to 1/√A

                           

Answer 2

Answer:

T = 2π √[m / A*rho*g]

Explanation:

Using restoring force formula we can easily find out the value of Time period.