Laws of floatation :
1. The weight of floating body is equal to the weight of liquid displaced.
2. The centre of gravity of the floating body and the centre of buoyancy (centre of gravity of displaced liquid) are in the same vertical plane.
Fraction of volume of the body outside the liquid:
When a body floats in a liquid with a part submerged in the liquid, the weight of the liquid displaced by the submerged part is always equal to the weight of the body...
A body of volume V and density \(\rho_b\) is floating in a liquid of density \(\rho\) with volume Vin immersed in the liquid.vout is volume outside of water.
weight of floating body =weight of liquid displaced.
mbg =mlg (Where mb mass of the body;mlmass of the liquid displaced)
\( \therefore V\rho _b = V_{in} \rho \)
\( \Rightarrow v_{in} \) = \( \frac{{v\rho _b }} {\rho } \)
\(
\therefore V_{out} = V - V_{in} = V\left( {1 - \frac{{\rho _b }}
{\rho }} \right)
\) or \(
f_{out} = \frac{{V_{out} }}
{{V_{in} }} = \left( {1 - \frac{{\rho _b }}
{\rho }} \right)
\)