A man is throwing rocks off a boat floating in the middle of a lake. The rocks sink quickly to the bottom of the lake.
Does the water level in the lake rise, fall, or stay the same after the rocks are thrown off the boat and sink to the bottom of the lake?
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Hint
Consider Archimedes’ principle and how the rocks affect the water level while they are on the boat vs. how the rocks affect the water level when they are in the lake.
Solution
The water level in the lake falls.
When an object is floating in water, like a rock in the boat, it displaces an amount of water with weight equal to the object’s weight. This is Archimedes’ principle.
When an object is submerged in water, like a rock at the bottom of a lake, it displaces an amount of water with volume equal to the object’s volume.
Since the rocks sank to the bottom of the lake, they must be denser than water, and thus they must displace more water when floating in the boat than when submerged. This means the water level was higher when the rocks were floating in the boat than when the rocks sank to the bottom of the lake.
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