Stability of a floating body: position of the metacentre A floating body will have stable equilibrium when the metacentre (M) is located where, relative to the body’s centre of gravity (G)?

Introduction / Context:Ship stability, pontoon design, and floating structures rely on metacentric height GM. The sign and magnitude of GM determine whether small angular disturbances are self-correcting (stable) or amplifying (unstable).

Given Data / Assumptions:

• Small heel angles (initial stability).
• Homogeneous fluid and standard hydrostatic definitions of G, B (buoyancy center), and M (metacentre).

Concept / Approach:

Initial stability criterion: GM = BM − BG. If GM > 0, the righting moment restores equilibrium. Geometrically, this is equivalent to metacentre M lying above center of gravity G for small angles.

Step-by-Step Solution:

Verification / Alternative check:

Righting arm GZ ≈ GM * sin θ for small θ. Positive GM yields positive GZ, giving restoring moment Δ * GZ (Δ is displacement).

Why Other Options Are Wrong:

M at G (GM = 0) is neutral, not stable. M below G is unstable. “Anywhere” and “at the waterline” do not reflect the hydrostatic stability criterion.

Common Pitfalls:

Confusing centroid with centre of gravity and with centre of buoyancy; only the position relative to G matters for initial stability.

Final Answer:

Above the centre of gravity (M above G)