Final answer:
Marbles in a bathtub experience buoyant force upon submersion, but when they sink to the bottom, the full weight of the marbles is transferred to the bottom of the tub. The actual downward force on the tub's bottom increases exactly by the marbles' weight due to the conservation of mass and is independent of the buoyant force.
Step-by-step explanation:
When marbles are dropped into a partially filled bathtub, they experience a force called the buoyant force which acts in the upward direction and is a result of the pressure difference between the top and bottom of the marbles while submerged in the water.
Despite this buoyant force, the total downward force on the bottom of the tub does increase by the exact weight of the marbles. This is because of the principle of conservation of mass. The marbles displace a volume of water equal to their own volume. The weight of this displaced water is equal to the buoyant force. However, since the marbles sink, it indicates that their weight is greater than the weight of the displaced water (the buoyant force). When the marbles reach the bottom of the tub, their full weight is transferred to the bottom.
Now, the water level rises very slightly when the marbles are submerged due to the displacement caused by the marbles. But the increase in water level does not change the weight of the water or the pressure exerted at the bottom of the tub. Therefore, the increase in downward force on the bottom of the tub can only be the weight of the marbles themselves. Thus, the principle of Archimedes' Principle complements the fact that the weight felt by the tub increases exactly by the weight of the marbles irrespective of the buoyant force provided by the fluid.