Floating bodies – Stability criterion using metacentre A floating body is said to be not in (stable) equilibrium if its metacentre M lies below its centre of gravity G. Do you agree with this statement?

Introduction:For floating bodies, small-angle stability is evaluated using the metacentric height GM, where G is the centre of gravity and M is the metacentre. The sign of GM determines the nature of equilibrium, which is critical for ship design, buoys, and pontoon platforms.

Given Data / Assumptions:

• Small angular displacement (initial stability).
• Homogeneous liquid; body floats partially submerged.
• Quasi-static conditions (no waves or dynamic effects).

Concept / Approach:

For small heel angles, the restoring moment per unit heel angle is proportional to GM. If GM > 0 (M above G), a restoring moment returns the body to its original position (stable). If GM = 0, the body exhibits neutral equilibrium. If GM < 0 (M below G), an overturning moment increases the displacement—this is unstable (i.e., not in stable equilibrium). Thus, the statement is correct.

Step-by-Step Solution:

Verification / Alternative check:

Ship stability textbooks use the righting arm GZ ≈ GM * sin(theta) for small theta. If GM is negative, the righting arm reverses sign, indicating capsizing tendency, confirming instability.

Why Other Options Are Wrong:

Disagree: Contradicts the metacentric height criterion.Angle or density caveats: Initial stability result holds without those extra restrictions.

Common Pitfalls:

Confusing small-angle (initial) stability with large-angle behavior; GM is strictly an initial stability parameter but suffices for the statement posed.

Final Answer:

Agree