Question:

When the rock is dropped from the boat into the pond, will the water level rise, fall or remain the same?

Answer:

When the 50-gram anchor was “floating” in the boat, it must be experiencing an upthrust that’s equal to its weight. So the anchor must have caused the boat to displace 50-grams of water. (Archimedes’ Principle)

When the 50-gram anchor was sunk at the bottom of the beaker, it must be experiencing an upthrust that’s less than it weight. So the anchor must have displaced less than 50-grams of water.

Since less water is displaced, the water level does not rise as much, and hence is lower.

Delving Deeper

Density of brass is about 9 g cm^-3. So the 50-gram brass weight has a volume of about 5.5 cm^-3. So it displaces only 5.5 cm^-3 of water when sunk, compared to 50 cm^-3 of water when it was floating in the boat.

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