What happens to the sea level when an object floats in it? Of course it rises.

The weight of the boat plus object is the same whether or not the object is in the boat, so the weight of water displaced, and the upthrust is the same.

The sea level does not change.

\[W=(M+m)g= \rho_{WATER}V_1 g \rightarrow V_1 =\frac{M+m}{\rho_{WATER}}\]

If the object is thrown out and sinks, then the weight of water displaced after it is thrown is less than before, since when the object is sinking, it only displaces its own volume of water, which weighs less than the weight of the object.

If the volume of the object is

\[V_{OBJECT}\]

the weight of water displaced by the object is \[V_{OBJECT} \rho_{WATER}\]

and the total weigght of water displaced is \[W=Mg+ \rho_{WATER} V_{SOLID} g =\rho_{WATER} V_2 g \rightarrow V_2 = \frac{M}{\rho} +V_{SOLID}\frac{M+m}{\rho_{WATER}}\]

In this case, volume of water displace is less and the sea level falls.