Buoyant force is defined as the upward force any fluid exerts on an object placed in it.

You know that fluids exert pressure. Archimedes, a Greek mathematician, discovered a fundamental principle known as Archimedes principle.

Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object.

Put simply, the magnitude of a buoyant force on an object always equals the weight of the fluid displaced by the object.

When an object immersed in a fluid reaches a level of equilibrium (no longer moving up or down), the upward buoyant force (B) of the fluid acting on the object is equal to the downward force acting on the object (weight – W).

The principle of buoyancy has many everyday applications.

Fish, in general, are slightly denser than water. But fish have a swim bladder which is adjusted by the fish to allow flotation at whatever level it chooses.

Checking the antifreeze in vehicles is an application of Archimedes principle. The simple device used in many places has small balls of different densities inside. If the liquid in your cooling system is pure water, all the balls float. If the liquid is pure antifreeze, none of the balls float. One floats at the density of a 5% mixture, one at the density of a 10% mixture, etc.

F_b = ρ_fluidVg

Always use the fluid density! The object volume and fluid volume will be the same if the object is totally submerged, so use either one!

Volume_under/Volume_material = density_material/density_liquid

OR

Height_under/Height_material = density_material/density_liquid

Ex: If salt water has a density of 1030 kg/m³, what percentage of an iceberg sticks up above the surface of the ocean?

Use the second equation and solve for the ratio of the height under to height of the material. You should find that 11% sticks up out of the ocean!

(source)