A Boat in a Tank

Imagine you are in a small rowboat floating in a swimming pool.  There's a big rock in the boat and you drop it overboard. Does the water level rise or fall?  Why?






Solution:
The water level will go down.  Imagine two rocks, the same size and shape, the only difference being that one of them is only slightly more dense than water, and the other is really really dense, made of lead.  When dropped into the pool, each rock will displace the same amount of water, because they have the same volume.  When something sinks, it displaces a quantity of water equal to its volume.  But when placed in a boat, the rocks are adding weight to a floating object - the boat.  Floating objects displace a quantity of water equal to their weight.  In the boat, the different rocks will have different effects.  The light rock won't make much difference - the boat will displace a bit more water than it would otherwise, making the water level rise slightly.  But the heavy rock will really weigh the boat down, causing it to displace a lot of water, and causing the water level to rise a lot. 

So to answer the question of what would happen if a rock was thrown off a boat, we need to compare displacement when the rock is in the boat (floating) to when the rock is at the bottom of the pool (sunk).  Since a rock is more dense than water, it has more weight than volume, relative to water.So more water would be displaced by its weigh than by its volume.  Therefore more water is displaced when it's in the boat than at the bottom of the pool; so when it's dropped overboard, less water is displaced and the water level goes down. 

The opposite would happen if you were chained to the bottom and pulled an empty two-liter bottle under the water.  First, it's only displacing water equal to its weight, because it's floating.  But then when you pull it under water, it's displacing water equal to its volume, which is much more.  Then the water level rises.