Q. Two solids $A$ and $B$ float in water. It is observed that A floats with $\frac{1}{2}$ of its body immersed in water and $B$ floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $A$ to that of $B$ is
A) 4 : 3
B) 2 : 3
C) 3 : 4
D) 1 : 2
Explanation
(b) Upthrust = weight of body
For $A,\frac{V_{A}}{2} \times \rho_{W} \times g = V_{A} \times \rho_{A} \times g \Rightarrow \rho_{A} = \frac{\rho_{W}}{2}$
For $B,\frac{3}{4}V_{B} \times \rho_{W} \times g = V_{B} \times \rho_{B} \times g \Rightarrow \rho_{B} = \frac{3}{4}\rho_{W}$
(Since 1/4 of volume of $B$ is above the water surface)
$\therefore\frac{\rho_{A}}{\rho_{B}} = \frac{\rho_{W}/2}{3/4\ \rho_{W}} = \frac{2}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.