A small ball of density ρ is immersed in a liquid of density σ ρ to a depth h and released. The height above the surface of water up to which the ball will jump is

Question

A small ball of density ρ is immersed in a liquid of density σ > ρ to a depth h and released. The height above the surface of water up to which the ball will jump is, σ ρ - 1 h, ρ σ - 1 h, ρ σ + 1 h, σ ρ + 1 h

MARKS App · Accepted Answer

Let V be the volume of the ball. New upward force = V σ g - V ρ g Net upward acceleration, a = V σ g - V ρ g V ρ = σ - ρ g ρ Velocity at the surface = 2 ( σ - ρ ) g h ρ If h a is the height in air to which the ball rises, then 0 - 2 σ - ρ g h ρ = 2 - g h a ∴ h a = ( σ - ρ ) g h g ρ = σ ρ - 1 h

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