Line of Action of Buoyant Force

Definition:
The buoyant force is the upward force exerted by a fluid on a submerged object, which opposes the gravitational force acting on the object.

Line of Action:
The line of action of the buoyant force is the vertical line passing through the center of gravity of the displaced fluid. It is the line along which the buoyant force acts on the object.

Displaced Volume of Fluid:
When an object is submerged in a fluid, it displaces an equal volume of fluid. The buoyant force acting on the object is equal to the weight of the displaced fluid. Hence, the line of action of the buoyant force passes through the center of gravity of the displaced fluid.

Centroid of the Displaced Fluid:
The centroid of the displaced fluid is the point at which the volume of the displaced fluid can be considered to be concentrated. It is the center of gravity of the displaced fluid. Hence, the line of action of the buoyant force passes through the centroid of the displaced fluid.

Volume of the Floating Body:
The buoyant force acts on the submerged volume of the object, which is equal to the volume of the displaced fluid. The line of action of the buoyant force passes through the centroid of this volume.

Volume of the Fluid Vertically Above the Body:
The volume of the fluid vertically above the body does not play any role in determining the line of action of the buoyant force. Therefore, option C is incorrect.

Submerged Body:
The line of action of the buoyant force does not necessarily pass through the centroid of the submerged body. The buoyant force acts on the displaced fluid, which may or may not be the same as the submerged body. Therefore, option A is incorrect.

Conclusion:
The correct answer is option D, i.e., the line of action of the buoyant force acts through the displaced volume of the fluid. It is important to understand that the buoyant force acts on the displaced fluid, and not on the submerged body. The line of action of the buoyant force passes through the centroid of the displaced fluid, which is the center of gravity of the volume of fluid displaced by the submerged object.