The iceberg has weight Wi = Mig and the buoyant force is equal to the weight of the displaced water, Ww = Mwg. Furthermore, since the iceberg is floating, its weight exactly balances the buoyant force:
Ww = Wi
Mwg = Mig
VwRhowg = ViRhoig
Vw = Rhoi/Rhow Vi
So, the fraction of ice underwater, Vw/Vi, is given by the ratio of densities Rhoi/Rhow=0.87. Over 87% of an iceberg's volume (and mass) is underwater. As you can see, the convenient definition of the gram gives us a quick way to see how much of a floating substance lies below the surface of fresh water: the fraction is equal to that substance's mass density in g/cm?.
Summary
Archimede's Principle of bouyancy states that the bouyant force on an object is equal to the weight of the fluid displaced by that object.The underwater fraction of a substance floating on water is given by that substance's mass density in g/cm3.
