A jar filled with two non mixing liquids 1 and 2 having densities $\rho_{1}$ and $\rho_{2}$ respectively. A solid ball, made of a material of density $\rho_{3}$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $\rho_{1}, \rho_{2}$ and $\rho_{3}$ ?

(D) $\rho_{1}<\rho_{3}<\rho_{2}$

(A) $\rho_{3}<\rho_{1}<\rho_{2}$

(B) $\rho_{3}<\rho_{2}<\rho_{1}$

(C) $\rho_{1}<\rho_{2}<\rho_{3}$

JEE Main · 2008 · 27 Apr 2008 · Offline · Fluid Mechanics

A jar filled with two non mixing liquids 1 and 2 having densities

ρ_{1}

and

ρ_{2}

respectively. A solid ball, made of a material of density

ρ_{3}

, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for

ρ_{1}, ρ_{2}

and

ρ_{3}

(A) $ρ_{3} < ρ_{1} < ρ_{2}$
(B) $ρ_{3} < ρ_{2} < ρ_{1}$
(C) $ρ_{1} < ρ_{2} < ρ_{3}$
(D) $ρ_{1} < ρ_{3} < ρ_{2}$ ✓ Correct

Answer: (D)

Solution

The ball settles at the interface, dipping into liquid 2 but riding on top of liquid 1. Resting on liquid 1 means liquid 1 is lighter than the ball (ρ₁ < ρ₃); failing to sink through liquid 2 means liquid 2 is heavier than the ball (ρ₃ < ρ₂). Liquid 1 itself floats above liquid 2, so ρ₁ < ρ₂. Chaining these gives ρ₁ < ρ₃ < ρ₂.

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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JEE Main · 2008 · 27 Apr 2008 · Offline · Fluid Mechanics

Solution

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