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What Happens to the Sea Level When an Object is Thrown From a Boat

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

What happens to the sea level when a passenger in a boat throws an object out of the boat, so that the object floats? The answer lies in Archimedes Principle, which states, 'the upthrust is equal to the weight of fluid displaced'
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.

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