A Trapped Boat

[BMAD]

Youre in a row boat, which is in a large tank filled with water. You have an anchor on board, which you throw overboard (the chain is long enough so the anchor rests completely on the bottom of the tank). Does the water level in the tank rise or fall?

[vistaptb]

it falls. When the anchor is in the boat, its weight is pushing down and displacing the water. When the anchor is out of the boat, its volume is displacing the water. Since the anchor is (presumably) denser than water, its relative weight should exceed its relative volume and thus push the water up further when it is in the boat.

[Debasis]

look down

Edited February 19, 2013 by Debasis

[Debasis]

if we use archimedes principle then i think it would not change...because upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid the body displaces.

[Bozo]

Debasis does state Archimedes principle correctly, But is that relevant here? Is the density of the anchor the key to this one?

If the weight and volume of the chain is negligible, then the anchor, resting "completely on the bottom of the tank" has effectively been thrown overboard - as the problem is stated its weight no longer is borne at all by the rowboat. Here only the weight of the rowboat (including that of the anchor) and the volume of the anchor affect the level in the tank. Let's assume that the iron anchor has a specific gravity of 8. It is pushing the boat down into the water 8 units when it's in the boat, displacing 8 units of water and raising the tank level by a proportionate amount. When thrown overboard it will displace 1 unit of water when it's immersed and no longer affect the boat's displacement. As stated by vistaptb: "its relative weight should exceed its relative volume and thus push the water up further when it is in the boat."

An intriguing twist might have the anchor still weighting the boat because the chain is too short to reach the bottom.

[ThunderCloud]

Although the Archimedes principle does apply. The volume of water displaced by the weight of the anchor in the boat is equal to the volume of water that would weigh the same as the anchor. Since the anchor is denser than water, this volume is larger than the volume of the anchor. Therefore, more water is displaced by the anchor's weight in the boat than by its volume in the tank, and the water level falls when the anchor drops.