Question

A jar is 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 ?

(a) ρ₁ <ρ₃ <ρ₂ 

(b)ρ₃ < ρ₁ < ρ₂

(c) ρ₁ > ρ₃ >ρ₂ 

(d) ρ₁ < ρ₂ < ρ₃

Answer 1

(a) : The liquid 1 is over liquid 2. Therefore ρ₁ <ρ₂. If ρ₃ had been greater than ρ₂, it will not be partially inside but anywhere inside liquid 2 if ρ₃ = ρ₂ or it would have sunk totally if ρ₃ had been greater than ρ₂.

Therefore,  ρ₁ < ρ₃ <ρ₂.