Suppose you have a ball made of a material with the same density as water, i.e. if submerged in water, the ball would neither sink nor rise. So if the ball is a sphere of the material, it stays in place in a column of water. If it’s full of a material with a lower density than water (e.g. air), it rises. If it’s full of a material with a greater density than water (e.g. iron), it sinks.
The question is, without changing the size of the ball, what happens if the middle of the sphere has no material at all, just vacuum? (Assume the material is strong enough to withstand the associated forces etc rigid and impermeable, so it doesn’t collapse the vacuum or fill it with anything, it’s a hard hollow ball with a vacuum inside – don’t buck the hypo)
My guess is entabbed below, but I am still uncertain.
[tab]It would rise, and faster/with more force than it did with air. My reasoning is that the sphere as a whole is less dense, as measured by mass/volume, i.e that vacuum is a very low density.
I confused myself (and hopefully some readers) by framing the setup as filling the ball with a ‘material’ that has higher density or lower density than water. That suggests a rule: whether it rises or falls is a function of the material’s density. In that frame, it’s uncertain what will happen to the ball when you remove all the ‘material’, because my rule was shitty and narrow – I think this is an example of overfitting, but I don’t know if I’m using that concept correctly.
But the rule should have been about the density of the ball as a whole. As far as the water is concerned, the ball is a black box; it doesn’t matter what the material is, it matters how much water the ball displaces and how much mass is contained in the displaced volume. In that framing, it seems that it would rise.
I’m still a little uncertain because it doesn’t seem like vacuum should float. It kind of makes sense that vacuum should repel matter that way, because that seems like another way to say “gravity”, but it’s still weird.[/tab]
[EDIT: clarified that the ball is rigid, per comment here]