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A ball is made of a material of density ρ, where ρₒᵢₗ<ρ<ρ_water, with ρₒᵢₗ and ρ_water representing the densities of oil and water respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following describes its equilibrium position?

Asked in AIEEE 2010 · Two liquids, cavities and relative density

• (1) Oil above water, with the ball floating on top of the oil.
• (2) Water above oil, with the ball floating on top of the water.
• (3) Oil above water, with the ball resting at the oil--water interface.
• (4) Water above oil, with the ball resting at the water--oil interface.

Step-by-step solution

Why the other options are wrong

• (1) comes from puts the layers the right way round but the ball on top of the oil; that would need ρ<ρₒᵢₗ, and the ball is denser than the oil, so it sinks through the oil layer.
• (2) comes from gets both things wrong: oil is the lighter liquid, so water cannot lie above it, and the ball is denser than oil so it cannot rest on any free surface here.
• (4) comes from has the ball in the right place but the liquids inverted; since ρₒᵢₗ<ρ_water, the oil must float on the water, not the other way round.

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