Buoyancy – line of action and center of buoyancy The line of action of the buoyant force (upthrust) on a submerged or floating body passes through the centre of gravity of the displaced liquid volume, i.e., the centroid of the displaced volume. State whether this statement is correct:

Introduction:
Buoyancy is the upward force exerted by a fluid on an immersed body. This question checks whether you know the exact point of application of the buoyant force and how it relates to the displaced fluid volume.

Given Data / Assumptions:

• Rigid body partially or fully immersed in a static fluid.
• Fluid is continuous and at rest; free surface may exist.
• Body may be in equilibrium or constrained; stability effects (metacentre) are discussed conceptually.

Concept / Approach:
Archimedes’ principle gives magnitude: buoyant force equals weight of displaced fluid. The line of action of this force passes through the centroid of the displaced volume of fluid, known as the center of buoyancy. For floating stability, the center of buoyancy shifts with heel, and the metacentre concept becomes relevant, but the buoyant force still acts through the instantaneous centroid of displaced volume.

Step-by-Step Solution:
1) Consider a body displacing volume V_d of fluid of specific weight w.2) Magnitude of buoyant force: F_b = w * V_d.3) Pressure forces act normal to the surface and integrate to a resultant acting vertically upward.4) Resultant line of action passes through the centroid of the displaced fluid volume (center of buoyancy).5) Therefore the given statement is correct.

Verification / Alternative check:
Hydrostatic pressure distribution increases with depth. Integrating pressure over the wetted surface yields a resultant that must pass through the centroid of the displaced volume because that is the balance point of the distributed pressures.

Why Other Options Are Wrong:

• False: contradicts the hydrostatic integration result.
• True only for incompressible liquids: gases also obey hydrostatics; the definition is geometric, not restricted to liquids.
• True only for gases at low pressure: unnecessary restriction; the result is general for fluids at rest.

Common Pitfalls:
Confusing center of buoyancy with center of mass of the body; mixing up metacentric height (stability) with buoyant line of action at a given heel.

Final Answer:
True