Question

A jar is filled with two non - mixing liquid 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 ${\rho }_1,{\rho }_2$ 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. ${\rho }_1<{\rho }_3<{\rho }_2$

Answer 1

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

${\rho }_1<{\rho }_2$ as denser liquid acquires lowest position of vessel.
${\rho }_3>{\rho }_1$ as ball sinks in liquid 1 and ${\rho }_3<{\rho }_2$ as ball doesn't sinks in liquid 2, so ${\rho }_1<{\rho }_3<{\rho }_2$