A neutral condition of stability corresponds to which relation between G and M?

• A. G=M
• B. M over G
• C. G over M
• D. G+M

Answer: (A)

The situation described is neutrally stable when the center of gravity sits exactly at the metacenter, so the metacentric height is zero. In naval stability terms, that means GM = 0, i.e., the distance between the center of gravity and the metacenter is zero, which occurs when G and M are at the same point.

Why this is the best choice: when the body tilts, the buoyant force shifts and a restoring or overturning moment depends on whether the center of gravity is below or above the metacenter. If G is below M, a righting moment acts to return upright; if G is above M, an overturning moment grows. Only when G coincides with M is there no restoring or overturning moment for small tilts, giving neutral stability.

Other alternatives don’t describe this zero-distance condition: a ratio like M over G or G over M implies a proportion, not a zero metacentric height; adding G and M doesn’t relate to stability at all.