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Mechanical Properties Of Fluids

Question

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A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?

ρ₃ < ρ₁ < ρ₂

ρ₁ < ρ₃ < ρ₂

ρ₁ < ρ₂ < ρ₃

ρ₁ < ρ₃ < ρ₂

Solution

D.

ρ₁ < ρ₃ < ρ₂

As liquid 1 floats above liquid 2,
ρ₁ < ρ₂
The ball is unable to sink into liquid 2, ρ₃ < ρ₂
The ball is unable to rise over liquid 1
ρ₁ < ρ₃ Thus, ρ₁ < ρ₃ < ρ₂

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