The metacenter M is defined as what?

• A. The point about which the ship rotates when it heels; GM is the distance from G to M.
• B. The center of gravity of the ship.
• C. The point where buoyancy acts when upright.
• D. The center of buoyancy.

Answer: (A)

The metacenter is the point about which the hull tilts when it heels a small amount; the distance from the center of gravity to that point (GM) is the metacentric height. As the ship heels, the center of buoyancy shifts to the low side, and the buoyant force acts through a new point. For a small angle of heel, the line of action of buoyancy intersects the vertical line through the center of gravity at the metacenter. This makes M the instantaneous pivot for small rotations due to buoyancy and weight.

If M lies above the center of gravity, the resulting moment tends to right the vessel and restore upright stability; if M is below G, the heel would be unstable. The center of gravity is a fixed point where weight acts, and the center of buoyancy is the shifting point where buoyancy acts with heel, so the metacenter is a distinct intersection that governs stability.