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An object of density d0 is held deep inside water of density dw and then released. As it moves a vertical distance h through the water, which statement is correct?

1. The gravitational potential energy of the water in the vessel increases if d0 < dw
2. The gravitational potential energy of the water in the vessel decreases if d0 < dw
3. The gravitational potential energy of the object increases if d0 > dw
4. The gravitational potential energy of the object decreases if d0 < dw

Correct answer: The gravitational potential energy of the water in the vessel increases if d0 < dw

Solution

If d0 < dw the object floats up. As the object (volume V) rises by h, an equal volume of water must move down to take its former place. But the object is lighter than water, so when this exchange happens the heavier water effectively moves up to fill above... carefully: the buoyant body rises, displacing water that flows down into the lower region the body vacated. The net effect raises the water column's effective distribution. By energy bookkeeping the gravitational PE of the water increases when a lighter object rises through it (the water's centre of mass rises). Hence option A is correct.

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