Rock in a boat and the water level

Question

You are sitting in a small boat that floats in a swimming pool. In the boat with you is a heavy rock. You pick up the rock and throw it overboard, and it sinks to the bottom of the pool.

Does the water level in the pool rise, fall, or stay the same?

Accepted Answer

Think about how much water the rock displaces in each situation. While in the boat (floating): the rock's weight is supported by the boat, so the boat sits lower and displaces an extra volume of water whose weight equals the rock's weight. A dense rock is heavy, so it displaces a large amount of water this way, a volume equal to (rock's weight) / (density of water). After sinking: the rock rests on the bottom and displaces only its own physical volume of water, (rock's mass) / (density of rock). Since the rock is denser than water, its own volume is smaller than the volume of water equal to i…

Rock in a boat and the water level

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