Determine the equation for the volume of the partially immersed part of a body floating in a fluid.

(N/A) When a body floats on the surface of a liquid,the weight of the body is equal to the weight of the liquid displaced by the body.
According to the principle of floatation: $W_{\text{body}} = W_{\text{displaced liquid}}$.
Let $V$ be the total volume of the body and $\rho$ be its density.
Let $V^{\prime}$ be the volume of the part of the body immersed in the liquid and $\rho_{l}$ be the density of the liquid.
The weight of the body is $W = V \rho g$.
The weight of the displaced liquid (buoyant force) is $F_{B} = V^{\prime} \rho_{l} g$.
Equating the two: $V \rho g = V^{\prime} \rho_{l} g$.
Thus,the ratio of the immersed volume to the total volume is given by: $\frac{V^{\prime}}{V} = \frac{\rho}{\rho_{l}}$.
Therefore,the volume of the immersed part is $V^{\prime} = V \left( \frac{\rho}{\rho_{l}} \right)$.