Explain the meaning of Buoyant Force (in a liquid) and how it relates to the weight of the object, as well as the weight of the displaced fluid.

The Buoyant Force, supposedly first observed by
Archimedes, is the upward force exerted upon a solid in a fluid, and can be expressed as
a ratio of densities between the fluid and solid.  Density, as you may know, is defined
as the mass divided by the volume, or D = m/v. Every solid has a mass and a volume, and
therefore the density can be calculated. A solid will float in a fluid if its density is
less than that of the fluid; it will conversely sink if its density is more than that of
the fluid. Floating implies that the solid displaces a weight of fluid greater than
itself; sinking implies it displaces a weight of fluid lesser than itself. Strictly
speaking, the weight of an object is not the same as the mass; mass is a singular
property expressed in kilograms or pounds; weight is actually a measure of a mass under
the force of gravity, given by the formula w = mg, where w is the weight, m is the mass,
and g is the force of gravity.