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A jar is filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. In the figure, liquid 1 forms the upper layer and liquid 2 the lower one. A solid ball, made of a material of density ρ₃, is dropped in the jar and comes to equilibrium resting at the boundary between the two liquids, part of it in each. Which of the following is true for ρ₁, ρ₂ and ρ₃?

Asked in AIEEE 2008 · Two liquids, cavities and relative density

• (1) ρ₁<ρ₃<ρ₂
• (2) ρ₃<ρ₁<ρ₂
• (3) ρ₁>ρ₃>ρ₂
• (4) ρ₁<ρ₂<ρ₃

Step-by-step solution

Why the other options are wrong

• (2) comes from makes the ball lighter than both liquids, which would float it on the free surface of liquid 1 rather than leave it at the interface.
• (3) comes from puts the lighter liquid at the bottom; the figure shows liquid 1 lying above liquid 2, so ρ₁<ρ₂, and this option reverses that.
• (4) comes from makes the ball denser than both liquids, which would send it to the bottom of the jar; it also mistakes 'partly in liquid 2' for 'sunk through liquid 2'.

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