Alright. Holding an iceberg under the ocean would be just like holding an ice cube in a coffee cup in the lab. Let me explain. Measure the water level in the coffee cup. Put the ice cube in. Push it down until it's completely submerged. Measure the water volume. Pull it out, melt it, and pour that water back into the cup. Measure the volume a third time. You will find that after you melt the ice cube and pour it back into the cup, the water level is LOWER than when you held the cube in.
Ice is less dense than water (which is why it floats). That means that a 1 pound of ice is actually physically bigger (has more volume) than when it's 1 pound of melted ice. Water expands when it freezes. It actually gets bigger. So the iceberg takes up more space frozen than it did when it wasn't frozen. Therefore... assuming the whole iceberg is underwater, the water level will actually go down a little as it melts.
Answered by: Frank DiBonaventuro, B.S., Air Force Officer, Physics grad, The Citadel
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'Physicists like to think that all you have to do is say, these are the conditions, now what happens next?'
Richard Phillips Feynman