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  4. 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, ρ1 and ρ3 ?

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Q. 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 the figure. Which of the following is true for $\rho_1, \rho_1$ and $\rho_3$ ?Physics Question Image

Mechanical Properties of Fluids

Solution:

From the figure it is clear that liquid $1$ floats on liquid
$2$. The lighter liquid floats over heavier liquid. Therefore we can conclude that $\rho_1<\rho_2$
Also $\rho_3<\rho_2$ otherwise the ball would have sink to the bottom of the jar.
Also $\rho_3>\rho_1$ otherwise the ball would have floated in liquid 1 . From the above discussion we conclude that
$\rho_1<\rho_3<\rho_2$