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 $2/3$ of its volume immersed. The ratio of their densities is

• A. 4 : 3
• B. 3 : 4
• C. 2 : 3
• D. 3 : 2

Answer 1

The correct option is B 3 : 4

Take equal volume of $A$ and $B$, say $V$.

Weight of $A=$ Weight of $\frac{V}{2}$ volume of water.

Similarly, weight of $B=$ Weight of $\frac{2V}{3}$ volume of water.

As density is weight per unit volume, the required ratio will be

$\frac{D_A}{D_B}=\frac{\left(V/2\right)}{\left(2V/3\right)}=\frac{3}{4}$

Thus, density of $A:$ density of $B=3:4$