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Q.

Density of a liquid varies with depth as . A small ball of density  is  released from the surface of the liquid. Then( is A positive constant)

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a

the ball will execute simple harmonic motion of amplitude ρ0α

b

the mean position of the ball will be at a depth ρ02α  from the free surface

c

ρ0αthe ball will sink to a maximum depth of

d

all of the above

answer is A.

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Detailed Solution

At equilibrium depth he, B = Buoyant force =
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Density of a liquid varies with depth as . A small ball of density  is  released from the surface of the liquid. Then( is A positive constant)