The mass of the boat is M and the mass of the rock is m. The density of water is Ļ_w and the density of the rock is Ļ_r.

When the rock is in the bock, Archimedeās Principle is the following case:

V_{d1} = \frac{(M + m)}{Ļ_w}

When the rock is at the bottom of the lake, Archimedeās Principle gives us this case:

V_{d2} = \frac{M}{Ļ_w} + \frac{m}{Ļ_r}

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

V_{d1} - V_{d2} = \frac{m}{Ļ_w} - \frac{m}{Ļ_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.**

1 Like