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

step 1 We have problem number 15. Question says that a jar is filled with two non -mixing liquids 1 and

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:(a) $\rho_{3}<\rho_{1}<\rho_{2}$ (b) $\rho_{1}>\rho_{3}>\rho_{2}$ (c) $\rho_{3}>\rho_{1}>\rho_{2}$ (d) $\rho_{2}>\rho_{3}>\rho_{1}$

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:(a) $\rho_{3}<\rho_{1}<\rho_{2}$
(b) $\rho_{1}>\rho_{3}>\rho_{2}$
(c) $\rho_{3}>\rho_{1}>\rho_{2}$
(d) $\rho_{2}>\rho_{3}>\rho_{1}$

Key Concepts

Equilibrium in Layered Fluids

Equilibrium in layered fluids involves an object finding a stable position where the net buoyant force is balanced by its weight. When an object is placed in a stratified system, such as layers of immiscible liquids, its final position is determined by its density relative to the densities of the individual liquids. It may float at the interface if its density lies between those of the two layers.

Density

Density is the measure of mass per unit volume of a substance. It is a fundamental property that determines how substances interact, especially in fluids, where the relative densities of different materials dictate whether an object will sink or float. This concept is central to understanding buoyancy and equilibrium in fluid mechanics.

Buoyancy

Buoyancy refers to the upward force exerted by a fluid that opposes the weight of an object immersed in it. According to Archimedes’ principle, the buoyant force is equal to the weight of the displaced fluid. This force determines whether an object will float, sink, or remain neutrally buoyant based on its density relative to the fluid’s density.

Immiscibility and Stratification

Immiscibility is the property of liquids that do not mix, leading to stratification where separate layers form based on differing densities. In a system with two immiscible liquids, the denser liquid settles at the bottom while the lighter liquid stays on top. This layering is crucial when analyzing how objects interact with each distinct layer.

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