You are in a rowing boat on a lake. A large heavy rock is also in the boat. You heave the rock overboard. It sinks to the bottom of the lake. What happens to the water level in the lake? Does it rise, fall or stay the same?

Archimede's Principle, Synapse PD, Apple

The mass of the boat is M and the mass of the rock is m. The density of water is ρ_w and the density of the rock is ρ_r.

When the rock is in the bock, Archimede’s Principle is the following case:

V_{d1} = \frac{(M + m)}{ρ_w}

When the rock is at the bottom of the lake, Archimede’s Principle gives us this case:

V_{d2} = \frac{M}{ρ_w} + \frac{m}{ρ_r}

If you take the difference of the two, you get:

V_{d1} - V_{d2} = \frac{m}{ρ_w} - \frac{m}{ρ_r}

The density of the rock is greater than the density of the water, making the above equation positive. This means that more water is displaced with V_{d1}. The water level falls when the rock is thrown overboard.

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