There's an old saying that if you are standing in a boat in the middle of a lake
and dropped a cannonball into the water, the water level would actually drop?
This seems contradictory to common sense because as we all know, when you drop an
object into a body of water the water level rises because of the volume of water
that the object displaces.
For example, if you fill your bathtub with water all the way to the brim and then
climb into the tub, the water will spill over the edge of the tub. This happens
because of the large amount of water that your body displaces when you jump in the
tub.
But the cannonball trick is indeed true. If you drop a cannonball in the lake, the
water level will drop. Here's why...
Wile the cannonball is in your boat, the great weight of the cannonball causes the
boat to displace quite a bit of water. Remember, Archimedes' principle states that
an object must displace its own weight in water. Since the cannonball is very dense,
the boat would displace around 10 cannonball volumes of water in order to maintain
the buoyancy needed to support the weight of the cannonball. Thus at this point,
the water level has risen.
Now we toss the cannonball over the edge of the boat. The boat will now float higher
than before because it does not need to displace the 10 cannonball volumes of water.
But, the cannonball is now displacing 1 cannonballs volume of water as it sinks
to the bottom of the lake. Now we are displacing 1 cannonball volume of water versus
the 10 cannonball volumes of water before (when the cannonball was in the boat).
That means we are actually displacing less water with the cannonball out of the
boat than we were with the cannonball in the boat. Thus the water level of the lake
actually rises.