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?
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6$\begingroup$ This is really a physics question, not a puzzle. $\endgroup$– BobsonCommented Oct 8, 2014 at 15:27
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2$\begingroup$ The water level will rise. He really should not have taken out the bung. $\endgroup$– kaineCommented Oct 8, 2014 at 18:29
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2 Answers
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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.
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1$\begingroup$ Since it is a stone (and presumably heavier than water! => How about Pumice where the exterior has been ground or waterproofed in some way? $\endgroup$ Commented Oct 8, 2014 at 18:47
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2$\begingroup$ @HostileFork Which is why I said "presumably" and not "definitely". Yes - I am making that assumption. $\endgroup$– TreninCommented Oct 9, 2014 at 11:36
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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
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$\begingroup$ Why would you repeat the same answer? $\endgroup$– MatsmathCommented Sep 13, 2016 at 20:59
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$\begingroup$ @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. $\endgroup$– smciCommented Sep 13, 2016 at 21:02