Final answer:
If a vessel sinks, its mass is greater than the mass of the fluid it displaces, resulting in a buoyant force that is less than the vessel's weight, consistent with Archimedes' principle.
Step-by-step explanation:
When comparing the mass of the vessel to the mass of the displaced fluid after sinking, the observation is that the mass of the vessel was greater than the mass of the displaced fluid. This implies that the buoyant force is less than the weight of the vessel. According to Archimedes' principle, the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. If an object sinks, its density is greater than the fluid, and therefore the weight of the fluid displaced is less than the weight of the object, which results in the buoyant force being insufficient to keep the object afloat.
The average density of an object determines whether it will float or sink. A floating object displaces a volume of fluid that weighs the same as the object, but a sinking object is unable to displace enough fluid to equal its own weight, leading to a buoyant force that is less than necessary for buoyancy.