Floating bodies – condition for stable equilibrium using metacentre A body floating in a liquid is said to be in stable equilibrium if its metacentre coincides with its centre of gravity. Is this statement correct?

Introduction / Context:
The stability of floating bodies (ships, pontoons, buoys) is assessed using the relative positions of the centre of gravity (G), centre of buoyancy (B), and the metacentre (M). Knowing the correct condition for stability is vital in naval architecture and hydraulic design.

Given Data / Assumptions:

• Small-angle stability analysis (metacentric theory).
• G is the centre of gravity; B is the centroid of displaced volume; M is the metacentre.
• Liquid is static; body floats freely without external constraints.

Concept / Approach:
For small heel (tilt), the restoring moment depends on the metacentric height GM = M − G (taking upward positive). The classical criterion states: stable equilibrium requires M above G (GM > 0). If M and G coincide (GM = 0), the body is neutrally stable; if M is below G (GM < 0), the body is unstable.

Step-by-Step Solution:

Verification / Alternative check:
A simple float model shows that when G is lowered or B is raised to place M above G, the body rights itself after a disturbance. When M drops to G, it neither rights nor overturns—neutral.

Why Other Options Are Wrong:

• “True” is incorrect; coincidence implies neutral equilibrium, not stable.
• Other options add conditions that are not the correct general criterion for stability.

Common Pitfalls:
Confusing the conditions for stability (M above G) with the condition for neutral equilibrium (M coincident with G).

Final Answer:
False