This month we have more of a question than a brain teaser. But, it definitely has a brain teaser-ish feel to it! Enjoy!
Suppose you are on a boat in the middle of a lake. There is an extremely heavy lead anchor in the boat. If you were to throw the anchor into the lake, would the water level rise, fall, or stay the same? Why?
Answer:
Initially, when the lead anchor is in the boat, the mass of the water displaced upward is equal to the mass of the anchor pushing down in the boat. But when the anchor is dropped into the water, the volume of water displaced is equal to the volume of the anchor. Since the anchor is much denser than the water, the amount of water equal to the mass of the anchor is greater than the amount of water equal to the volume of the anchor. Thus, when the anchor is thrown into the water there will be less water displaced and the water level of the lake will fall.
Essentially, it is a matter of mass vs. volume. It might help to take an extreme example to illustrate why the water level will fall. If the anchor was tiny (like the size of a quarter) but weighed as much as a normal anchor, it should be clear that when you throw the tiny anchor into the water not much will be displaced (since that is a function of its size or volume). But if the anchor is extremely heavy, it will push down significantly into the boat and thus into the water, displacing a lot of water upwards.