Question

Does the water level rise, fall, or remain the same when the anchor is dropped into the water from the boat? Why?

Answer

As you can see from the video, dropping the anchor from the boat into the water causes the water level to fall.

The outcome is obvious if we compare the amount of upthrust in the two scenarios.

When the anchor is sunk, the total upthrust must be smaller than when it is floating (since upthrust is now insufficient to support the anchor’s weight). Smaller upthrust implies less water displaced and thus a lower water level.

To be more specific, the volume of water displaced by the anchor when it is floating is 50 cm^-3 (see 0:22), corresponding to 50 g of water. (This is just enough upthrust to support the anchor’s weight.)

The volume of water displaced by the anchor when it is sunk is less than 10 cm^-3 (see 0:43). This is actually the anchor’s volume, and it corresponds to less than 10 g of water. (The amount of upthrust generated is not enough to support the anchor’s weight. Which is why it sinks)

Since less water is displaced, the water level does not rise as high.

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