Question

An ocean going barge with pig iron was in a lock. (If you prefer, think of the lock as a giant bathtub). Assume the top of the barge is exactly 1 foot below the top of the lock (or top of the bathtub). The captain threw all the iron overboard. Did the barge go up or down or stay the same, relative to the top of the lock? What happened to the water level of the lock?

Answer 1

(a)

When captain threw all the iron overboard, the barge will go up as the force acting downwards is reduced by the removal of iron.

(b)

When an object sinks in water it necessarily displaces its own volume.
So when the iron is in the boat it is displacing its own mass equivalence in water. When the iron is thrown inside the lock, it is displacing its own volume in water.
So which of these is greater?
Well, we know the iron is denser than water because it sinks. So the volume of water equivalent to the mass of the iron is greater than the volume of the iron. And so less water is displaced after than before. Hence...The Water Level of the Lock Goes Down!