Question

Two uniform solids $A$ and $B$ having same volume, float in water. It is observed that $A$ floats with half of its volume immersed and $B$ floats with $\frac{2}{3}rd$ of its volume immersed. Find the ratio of mass of $A$ to $B$.

• A. $\frac{3}{4}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{3}{4}$

Let $V$ be the volume of the body and $\rho$ be the density of water.

Buoyant force acting on block $A;$ $F_A=\frac{1}{2}V\rho g=m_{A}g.....\left(i\right)$
Buoyant force acting on block $B$ $F_B=\frac{2}{3}V\rho g=m_{B}g.....\left(ii\right)$
From equation $\left(i\right)$ and $\left(ii\right)$,
$\frac{m_A}{m_B}=\frac{\frac{1}{2}V\rho g}{\frac{2}{3}V\rho g}=\frac{3}{4}$