The buoyant force is the force that acts on the object submerged or partially submerged in liquid. It is always directed up (as if to push the object out) and its magnitude can be determined from considering how the pressure inside the liquid changes with its height.
The magnitude of the buoyant force is
`F_b = rho*g*V` . Here, `rho` is the density of the liquid, g is the gravitational acceleration, and V is the volume of the submerged part of the object.
Thus, the factors determining the buoyant force are the density of the liquid, gravity, and the submerged volume.
Notice that if the above formula is rearranged as
`F_b = rhoV*g` , the product of the liquid density and the submerged volume make up the quantity equal to the mass of the liquid which would fill the submerged volume. The buoyant force, then, equal the weight of the liquid that would fill the submerged volume. This is known as the Archimedes' principle.
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