Question

A jar is filled with two non-mixing liquids 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 attains equilibrium in the position as shown in the figure. Which of the following is true for ${\rho }_1,{\rho }_2$ and ${\rho }_3$ ?

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

Answer 1

The correct option is D

${\rho }_1<{\rho }_3<{\rho }_2$

As liquid 1 floats above liquid 2, ${\rho }_2>{\rho }_1$.
As the ball doesn't sink into liquid 2, ${\rho }_3<{\rho }_2$.
Also, as the ball doesn't float in liquid 1, ${\rho }_3>{\rho }_1$.
Hence, ${\rho }_1<{\rho }_3<{\rho }_2$