Question

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 as shown in the figure. Which of the following is true for ${\rho }_1,{\rho }_2$ and ${\rho }_3$ ?

• A. ${\rho }_1<{\rho }_2<{\rho }_3$
• B. ${\rho }_1<{\rho }_3<{\rho }_2$
• C. ${\rho }_3<{\rho }_1<{\rho }_2$
• D. ${\rho }_1>{\rho }_3>{\rho }_2$

Answer 1

The correct option is B ${\rho }_1<{\rho }_3<{\rho }_2$

Let us try to write the situation mathematically,
${\rho }_{3}V=\frac{{\rho }_{1}V}{2}+\frac{{\rho }_{2}V}{2}$, [equilibrium weight and upthrust]-----------------(1)
and also, ${\rho }_1<{\rho }_2$ because liquid 1 is floating above liquid 2.
and from (1) it is pretty clear that ${\rho }_3$ should be in middle of ${\rho }_1$ and ${\rho }_2$
So,
${\rho }_1<{\rho }_3<{\rho }_2$