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

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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 equilibrium in the position shown in the figure. Which of the following is true for $\rho_{1}, \rho_{2}$ and $\rho_{3} ?$ (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 equilibrium in the position shown in the figure. Which of the following is true for $\rho_{1}, \rho_{2}$ and $\rho_{3} ?$
(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 the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by that object. In contexts involving multiple fluid layers, the net buoyant force is determined by the sum of the contributions from each fluid, which is crucial in understanding how objects come to rest at equilibrium positions.

Density and Buoyancy

The density of an object relative to the densities of the surrounding fluids determines whether it sinks, floats, or remains suspended. An object will sink in a fluid if its density is higher than that of the fluid, float if lower, and achieve neutral buoyancy when its density falls between the densities of two stratified fluids.

Stratification in Fluids

Stratification occurs when fluids with different densities do not mix, resulting in distinct layers with the heavier fluid at the bottom and the lighter fluid at the top. This separation affects the behavior of objects immersed in the fluids, as they may experience different buoyant forces in each layer, leading to equilibrium positions at the interface.

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