Define metacenter and GM.

• A. M is the point where the buoyant force acts when the ship heels; GM is the distance between the center of gravity G and the metacenter M.
• B. The center of gravity is the metacenter; GM is the distance to the stern.
• C. The center of buoyancy is the metacenter; GM is the distance to the bow.
• D. The metacentric axis is the balance point; GM is the hull's height.

Answer: (A)

Stability in a tilted ship comes from how buoyancy and weight create a restoring moment. The metacenter is the point about which the hull tends to rotate when the vessel heels a small amount. As the ship heels, the center of buoyancy shifts, and the line of buoyant force intersects the ship’s vertical through the center of gravity at that metacenter. The metacentric height, GM, is the vertical distance between the center of gravity and this metacenter.

Why this fits best: describing M as the point about which the hull tilts for small angles captures its role in generating the restoring couple, and defining GM as the distance between G and M ties the stability measure directly to how heavy the ship sits relative to that balance point. If M is above G (positive GM), the buoyancy and weight create a righting moment to return upright; if M were below G, the moment would tend to capsize.

The other statements mix up where the metacenter lies or what GM measures (not a distance to the stern or bow, not the center of gravity equaling the metacenter, and not the hull height).