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A uniform vertical U-tube has mercury at the bottom and water poured over it, with the water level equal in both arms. A piece of wood is dropped into one arm, and into the other arm an amount of water whose weight equals the weight of the wood is added. Consider: (I) The mercury level remains equal in both arms. (II) The water level remains equal in both arms. Which is/are true?
- Both I and II are true
- I is true but II is false
- I is false but II is true
- Both I and II are false
Correct answer: I is true but II is false
Solution
The floating wood transmits a downward force equal to its weight to the liquid below; the added water in the other arm also weighs the same. So mercury experiences equal additional pressure on both arms -> mercury stays level (I true). However, the wood floats and displaces a volume of water, raising the water column more (the wood plus displaced water occupies the arm), while the other arm just has the added water; the water levels are no longer equal (II false).
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