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