the buoyant force
The buoyant force is the upward push a fluid gives to anything placed in it. It is why a beach ball leaps back up when you release it underwater, why you feel lighter in a swimming pool, and why boats float. It answers the question: why does a fluid seem to hold objects up, partly or wholly against their weight?
The precise origin is the way pressure grows with depth. Every submerged object is squeezed by the fluid on all sides, but the pressure on its lower surface is greater than on its upper surface, because the bottom is deeper. The pressure forces therefore do not cancel; they leave a net upward push, and that leftover is the buoyant force. Its size is given by Archimedes' principle: the buoyant force equals the weight of the fluid the object pushes out of the way, F_b = rho_fluid × V_displaced × g, where rho_fluid is the fluid's density, V_displaced is the volume of fluid displaced, and g is the acceleration due to gravity.
Whether something floats or sinks is a contest between this upward buoyant force and the object's downward weight. If the object is less dense than the fluid, buoyancy wins and it floats; if denser, weight wins and it sinks. One honest point often missed: the buoyant force acts on a sinking object too, it does not vanish, it is simply not enough to hold the object up. This is why a rock feels lighter under water than in air.
A rock of volume 0.002 m^3 lowered into water displaces 0.002 m^3 of water, giving a buoyant force of F_b = rho g V = 1000 × 9.8 × 0.002 ≈ 20 N upward. If the rock weighs 50 N, its apparent weight under water is only 50 − 20 = 30 N.
The upward buoyant force reduces an object's apparent weight by the weight of the fluid it displaces.
The buoyant force acts on sinking objects too; it does not disappear when something sinks, it is simply smaller than the object's weight. It comes from pressure being higher lower down.