Hydrostatics concept check: what is the correct definition of the centre of buoyancy for a floating or submerged body?

Introduction / Context:
The behaviour of floating and submerged bodies—stability, trim, and righting moments—depends on the relative locations of three key points: the centre of gravity (G), the centre of buoyancy (B), and for floats/ships, the metacentre (M). Understanding what B represents is fundamental to naval architecture and hydraulic design.

Given Data / Assumptions:

• Static conditions in a homogeneous, incompressible fluid.
• Body either fully submerged or floating in equilibrium.
• Gravity acts uniformly; pressure distribution is hydrostatic.

Concept / Approach:

Buoyant force equals the weight of the displaced fluid and acts upward through a specific point. That point is the centroid of the displaced fluid volume, known as the centre of buoyancy B. It is not the body’s centroid (unless densities and shapes cause coincidence by chance) nor the centre of pressure, which pertains to distributed forces on surfaces and depends on the second moment of area and depth.

Step-by-Step Solution:

Verification / Alternative check:

Archimedes’ principle provides magnitude of buoyant force; hydrostatic pressure integration over the wetted surface shows resultant passes through the centroid of displaced volume, confirming the definition.

Why Other Options Are Wrong:

(a) Centre of gravity of the body depends on mass distribution, not displaced liquid. (c) Centre of pressure is a different hydrostatic resultant point on a surface, not the line of action of buoyancy in general. (d) and (e) are unrelated or misleading descriptions.

Common Pitfalls:

Confusing B with G; assuming B is fixed (it shifts as the submerged geometry changes during heel or sinkage).

Final Answer:

The centroid of the displaced fluid volume.