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Consider the total gravitational potential energy of the water/bubble system. Since water is more dense than air, the bubble has less mass than the equivalent volume of water. So, if the bubble could rise a little the increase in potential energy of the air would be more than compensated for by the decrease in potential energy of the water.

This (rather simple) argument shows that the total potential energy of the system decreases as a function of the bubble's height, and thus the bubble rises through the water. More generally, it predicts that any object placed into a fluid of greater density should rise.

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