A jar is filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2, respectively. A

step 1 The given question, we are given two liquids of densities row 1 and row 2. This is liquid first,

A jar is filled with two non-mixing liquids 1 and 2 having...

A jar is 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 Fig. 8.50. Which of the following is true for $\rho_{1}, \rho_{2}$ and $\rho_{3} ?$ $[2007]$ Fig. $8.50$ (A) $\rho_{3}<\rho_{1}<\rho_{2}$ (B) $\rho_{1}>\rho_{3}>\rho_{2}$ (C) $\rho_{1}>\rho_{2}>\rho_{3}$ (D) $\rho_{1}<\rho_{3}<\rho_{2}$

A jar is 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 Fig. 8.50. Which of the following is true for $\rho_{1}, \rho_{2}$ and $\rho_{3} ?$
$[2007]$
Fig. $8.50$
(A) $\rho_{3}<\rho_{1}<\rho_{2}$
(B) $\rho_{1}>\rho_{3}>\rho_{2}$
(C) $\rho_{1}>\rho_{2}>\rho_{3}$
(D) $\rho_{1}<\rho_{3}<\rho_{2}$

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Key Concepts

Archimedes' Principle

This principle states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. In the context of buoyancy, it is used to determine whether an object will float, sink, or remain in equilibrium based on the relationship between the object's weight and the weight of the displaced fluid.

Density and Buoyancy

Density is defined as mass per unit volume and is a key factor in determining buoyant behavior. An object will float if its density is less than that of the surrounding fluid, sink if it is greater, and remain suspended when its density falls between the densities of two stratified fluids, allowing portions of the object to be in each fluid layer.

Equilibrium in Stratified Fluids

In systems with two immiscible fluids of different densities, an object can come to equilibrium at the interface if its density is intermediate between the two fluids. This results in a situation where part of the object displaces the lighter fluid and part the heavier fluid, balancing the forces of gravity and buoyancy to maintain equilibrium.

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