# Ship and stone puzzle

A floating ship contains one stone. The captain sees the stray stone and throws it into the water. What result will this action have on the water level? Will it increase or decrease?

• This is really a physics question, not a puzzle. – Bobson Oct 8 '14 at 15:27
• The water level will rise. He really should not have taken out the bung. – kaine Oct 8 '14 at 18:29

The water level will fall.

The reason for this is that the stone while in the boat is displacing water equal to its weight. For example, say the stone weighs 1 kilogram. It would displace one litre of water while in the boat because the boat is at equilibrium.

Now, if you take the stone out of the boat and put it in the water, you are losing the 1 litre of displacement you had while the stone was in the boat, but gaining the volume of the stone in displacement. Since it is a stone (and presumably heavier than water!) it has a higher density than water, so its displacement is less than 1 litre.

Thus, you are now displacing less water, so the water level will drop.

• Since it is a stone (and presumably heavier than water! => How about Pumice where the exterior has been ground or waterproofed in some way? – HostileFork says dont trust SE Oct 8 '14 at 18:47
• @HostileFork Which is why I said "presumably" and not "definitely". Yes - I am making that assumption. – Trenin Oct 9 '14 at 11:36

Depends on the density (ρ) of the stone, whether it's >1 or not:

While resting on the floating ship, the stone displaces water of equal weight W = ρV. When immersed, it displaces water of equal volume V. The delta in volume is (ρ-1)V

If ρ>1 (as is normal for stones, except e.g. pumice), then the former weight is greater, hence the water will slightly fall

If ρ<1 (exceptionally rare for stones), then the water will slightly rise

• Why would you repeat the same answer? – Matsmath Sep 13 '16 at 20:59
• @Matsmath I did not repeat the same answer. a) I pointed out there are actually two answers, although the relative-density<1 case is very rare. But possible. b) I put symbols on the quantities. Makes discussion clearer. – smci Sep 13 '16 at 21:02