Does the ship’s center of gravity move when cargo is moved from the bow of the ship to the stern?

Let us direct the x-axis from the bow to the stern.

Let the center of gravity of the vessel have a coordinate xk, and the cargo xg.

Weights of the vessel and cargo: mk and mg.

Coordinate of the general center of gravity of the vessel and cargo:

x1 = (mkxk + mhxg) / (mk + mg).

When the load moves along the x-axis at a distance a, the coordinate of the center of gravity will be written as:

x2 = (mkxk + m (xg + a)) / (mk + mg).

x2 – x1 = (mkxk + m (xg + a)) / (mk + mg) – (mkxk + mgxg) / (mk + mg) = mga / (mk + mg).

The difference between the coordinates of the center of gravity of the system before and after the movement of the load is not zero.

Answer: The position of the center of gravity moves when moving the load.