When a body is partially or completely immersed in a liquid, two forces act on it.
( i ) Weight of the body, W = ρs g Vs ↓ and ( ii ) Buoyant force, Fb = ρ f g Vf ↑
Here, ρs and Vs are the density and volume of the solid body, while ρf and Vf are the density and volume of the displaced liquid respectively. When the body is fully immersed in the liquid, Vs = Vf ( provided the solid body is not hollow or has no cavities ).
If W > Fb, the body sinks. If W = Fb, the body remains in equilibrium at any depth. Submarine works on this principle.
If W < Fb, the body floats in liquid and if its partially immersed volume is Vp, then the buoyant force Fb = ρf g Vp balances the weight W of the body.
Therefore W = Fb which implies ρs g Vs = ρf g Vp.
Thus, “ When the weight of a body is equal to the weight of the liquid displaced by a part of the body immersed in it, the body floats on the surface of the liquid.”
This statement is called law of floating
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