Cannonball logic

Following on from the last post, the podcast also has a logic puzzle, and last week’s question was:

You’re in a boat that’s floating in a pond. You’re holding a cannonball. If you drop the cannonball over the side, will the level of the pond rise, fall or remain the same?

Mr Thinks-he-has-a-good-knowledge-of-physics here got it completely wrong, because I didn’t think it through properly. There’s no trick – cannonballs don’t float or anything – it’s pure science. What do you think? Highlight below for the answer.

Answer: The level of the pond goes down. When in the boat the weight of the cannonball displaces a certain amount of water. But when in the water it’s only the volume that matters – water doesn’t care about the density (and therefore the mass, and therefore the weight) of what’s in it, just the space it takes up. A cannonball is obviously more dense than water, so the volume displaces less water than the weight, so the water level goes down. I fully expected the level to stay the same, thinking that the displacement wouldn’t change. If not that, then maybe it’d go up. Going down was my last choice by a long way.