Question

A beaker is filled with two nonmixing 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 beaker. It comes in equilibrium position after few seconds. Which of the following relation is true?

• A. $\rho_{2}>\rho_{3}>\rho$
• B. $\rho_{3}>\rho_{2}>\rho_{1}$
• C. $\rho_{1}>\rho_{2}>\rho_{3}$
• D. None

Answer 1

Answer: (A)

Let $V$ is the volume of ball and $m$ is the mass of ball
then, for equilibrium condition
$mg =\left( m _{1}+ m _{2}\right) g$
$V \rho_{3} g =\frac{ V }{2} \rho_{1} g +\frac{ V }{2} \rho_{2} g$
$\rho_{3}=\frac{\rho_{1}+\rho_{2}}{2}$
Now, we can say that density of ball is intermediate or average of $\rho_{1} \& \rho_{2}$ but from diagram it is clear that
$\rho_{2}>$ $\rho_{1}$ so $\rho_{2}>\rho_{3}>\rho_{1}$