The principle that explains the floating and sinking of objects in a fluid is known as Archimedes' principle. It states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. This principle helps determine whether an object will float or sink based on its density relative to the fluid's density. Objects with a density lower than the fluid will float, while those with a higher density will sink. Archimedes' principle is essential in fields such as hydrodynamics and engineering, informing the design of ships, submarines, and other floating structures.