Let m = mass of the body (object) immersed in the fluid, V = volume of the body, ρ = density of the body, ρ1 = density of the fluid, g = magnitude of the acceleration due to gravity. Suppose that the body is completely immersed in the fluid. Then the volume of the fluid displaced by the body = V. According to Archimedes’ principle, magnitude of the buoyant force = magnitude of the weight of the fluid displaced by the body = mass of the displaced fluid × g = volume of the displaced fluid × density of the fluid × g
(as density = mass/volume)
= V \(\rho_1g\) = \((\cfrac{m}{\rho})\) \(\rho_1g\)
= mg \((\cfrac{\rho_1}{\rho})\)
( ∵ \(\rho\) = \((\cfrac{m}{V})\))
If the body is partially immersed in the fluid, the volume of the fluid displaced by the immersed part of the body = xV ; here 0 < x < 1.
In this case, the magnitude of the buoyant force
