We are now able to understand why some
things float and some things do not. Consider some
small volume, V, of liquid within a larger volume of liquid at rest.
The forces acting on the volume of liquid are gravity and a force
generated by the surrounding liquid. Because the volume of liquid is
at rest these forces must exactly cancel which means that the force
exerted on the volume element by the surrounding fluid
equals the gravitational force:
This so-called buoyant force will be no different if I occupy the volume by
another material. Denote the density of that other material by 
then the net force on it will be
which implies that
if 
the object sinks while if
it will float towards the top of the liquid.