First slide

Fluid statics

Question

Two solids A and B float in water. It is observed that A floats with half of its volume immersed and B floats with $\frac{2}{3}$ of its volume immersed. The ratio of densities of A and B is

Moderate

A

4 : 3
B

3 : 4
C

3 : 2
D

2 : 3

Solution

$V_{A} ρ_{A} = \frac{1}{2} V_{A} \times 1 or ρ_{A} = \frac{1}{2}$
Again, $V_{B} ρ_{B} = \frac{2}{3} V_{B} \times 1 or ρ_{B} = \frac{2}{3}$
$\frac{ρ_{A}}{ρ_{B}} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

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