(a) The principle used to check the purity of milk is the specific gravity of Archimedes Principle. It checks the relative density of milk with respect to water.
(b-1)The principle is used to check the purity of different substances.
(b-2)By using Specific Gravity to our advantage, we keep the specific gravity of ships and boats less than 1 (i.e. less dense than water) to keep them floating on water.