A body of density ' ρ ' is dropped from rest at a height ' h ' into a lake of density ' σ ' ( σ ρ ) . The maximum depth to which the body sinks before returning to floa

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A body of density ' ρ ' is dropped from rest at a height ' h ' into a lake of density ' σ ' ( σ > ρ ) . The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces)

TestHub · Accepted Answer

Initial velocity of the ball = 2 gh ​ Upward force: ∴ ​ F = σV g − ρ V g ( ρ V ) a = V g ( σ − ρ ) a = ρ g ( σ − ρ ) ​ ​ Final velocity is zero when it sinks. ∴ ​ v 2 − u 2 = 2 as 0 − ( 2 g h ​ ) 2 = 2 ρ g ( σ − ρ ) ​ H H = ( ρ − σ ) h ρ ​ ​

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