Archimedes' principle - Why does an iceberg float?

Problem statement:

An iceberg is a large mass of freshwater that floats because ice density is smaller than that of seawater. Using Archimedes’ principle, estimate the fraction of the volume of an iceberg that is underwater to prove that 90% of it lies below the water line.
Givens: ρs = 1030 kg/m3; ρi = 0.920 g/cm3

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Solution:

We are going to apply Archimedes’s principle to solve this problem. For the iceberg to be in equilibrium, its weight must equal the buoyant force exerted by seawater. The latter is the weight of the volume of seawater displaced by the fraction of the iceberg immersed in the sea.

In the figure above the forces acting on the iceberg (its weight P) and the buoyant force F) are shown. The total volume of the iceberg is VT and the immersed volume of the iceberg is VS.

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In equilibrium:

On the other hand, the mass (m) of the iceberg is equal to its density ρi multiplied by its total volume. Substituting:

Converting both densities to SI units (kg/m3):

So 90% of the iceberg is underwater.

The expression above allows to estimate the fraction of any object immersed in a fluid, provided that both the density of the object and the fluid are known.

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