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A boat loaded with scrap iron floats on the water of a lake. If all the iron is taken out of the boat and dropped to the bottom of the lake, what happens to the water level of the lake?
- rises
- falls
- stays the same
- cannot be determined
Correct answer: falls
Solution
Floating: the iron in the boat displaces a water volume whose weight equals the iron's weight, i.e. volume = m/(rho_water). Since iron is denser than water, this displaced volume is larger than the iron's own volume. When dropped in, the submerged iron displaces only its own (smaller) volume. Therefore total displaced volume decreases, and the water level falls.
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