Hydrostatics & Stability – Correct Statement for Floating/Submerged Bodies Which of the following statements correctly states the stability condition for bodies that float or are wholly submerged in a liquid?

Introduction / Context:
Stability of bodies in fluids depends on the interplay between weight (acting at the centre of gravity, G) and buoyancy (acting through the centre of buoyancy, B) and, for floating bodies, the metacentre, M. A correct understanding of these concepts is essential for naval architecture and hydraulic engineering.

Given Data / Assumptions:

• Floating body: partially submerged, free surface present.
• Submerged body: completely below free surface.
• Small angular disturbances considered.

Concept / Approach:

For floating bodies, the criterion for initial (metacentric) stability is M above G (M > G). The relative position of B to G can vary; it is not the defining criterion. For completely submerged bodies, stability results when B above G (i.e., G is below B), because the buoyant force does not create a restoring couple unless the weight acts below the buoyancy line of action.

Step-by-Step Solution:

Verification / Alternative check:

Metacentric height GM = BM − BG; GM > 0 is the initial stability condition. For floating bodies, BM depends on waterline area moment of inertia; BG depends on geometry and mass distribution.

Why Other Options Are Wrong:

• Options a and b: Having B below G implies instability for submerged bodies and is not a stability criterion for floating bodies.
• Option c: Ignores the need for M > G; incorrect.

Common Pitfalls:

Confusing submerged-body criterion (B above G) with floating-body metacentric stability; assuming B must always be above G for floating bodies.

Final Answer:

For a body floating in a liquid, stability is ensured if the metacentre lies above the centre of gravity; having the centre of buoyancy below the centre of gravity also satisfies this sufficient condition.