# Floating and immersion

Question: How does the fraction of the submerged part of a floating object compare with the ratio of its density and the density of the liquid in which it floats?

The answer all depends on Archimedes principle. This states that:

When a body is totally or partially immersed in a fluid there is an upthrust which is equal to the weight of the fluid displaced.

Therefore if an object is floating the upthrust must equal the weight of the object.

Therefore:

Volume of displaced fluid (v) x density of fluid x g = Volume of object (V) x density of object x g

And this gives:
Volume of displaced fluid x density of fluid = volume of object x density of object

The ratio that you wanted is then:
Volume of submerged part of object/volume of object = density of object/density of fluid

Therefore for sea water (density 1100 kg/cubic metre) and ice (920 kg/cubic metre) the ratio is:

920/1100 = 0.84 and so 84% of the ice is below the level of the water.

© Keith Gibbs 2011