Final answer:
Marbles sink to the bottom of the bathtub because their weight is supported by the buoyant force exerted by the water. The downward force on the bottom of the tub increases by exactly the weight of the marbles. This is also true for other objects, such as clay boats and steel ships.
Step-by-step explanation:
When marbles are dropped into a partially filled bathtub, they sink to the bottom due to the principle of buoyancy. Part of their weight is supported by the buoyant force exerted by the water. The downward force on the bottom of the tub increases by exactly the weight of the marbles because the marbles displace an equal volume of water, which in turn exerts a downward force on the bottom of the tub.
For example, when a lump of clay is dropped in water, it sinks. However, when the same lump of clay is molded into the shape of a boat, it floats. This is because the boat displaces more water than the lump, and therefore experiences a greater buoyant force. The same principle applies to steel ships, which are able to float despite being denser than water.
In the case of the leaves sinking to the bottom of the beaker, it is likely that they were denser than the liquid in the beaker, causing them to sink. The buoyant force exerted by the liquid may not have been enough to support their weight.