Boat, Boulder, and Lake

A boat carrying a large boulder is floating on a lake. The boulder is thrown overboard and sinks to the bottom. The water level in the lake (with respect to the shore)

A) rises.

B) drops.

C) remains the same.

D) can't be determined.

Solution: B. When it is inside the boat, the boulder displaces its weight in water. When it is thrown overboard, it only displaces its volume in water so the water level of the lake with respect to the shore goes down.

You might also look at a free body diagram and Newton's second law for the boat and boulder as a system. Before the boulder is thrown overboard, there are only buoyant and weight forces. After the boulder comes to rest on the bottom of the lake, there is a normal force on the boulder. The buoyant force is therefore smaller, thus the volume displaced must be smaller. While the boulder is moving down, there is an upward drag force and a similar analysis holds, so you don't need to wait until the boulder hits the bottom to see the effect on the water level.