Question

why displaced water is equal to bouyant force

Answer 1

The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV. The fluid displaced has a weight W = mg, where g is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as W = ρVg.
Since pV = mass of the object so pVg= weight of object