Buoyant Force Explained

The concept of buoyant force is fundamental in fluid mechanics, particularly when dealing with floating or submerged bodies. Buoyant force is the upward force exerted by a fluid that opposes the weight of an immersed object. This principle is famously described by Archimedes' Principle.

Archimedes' Principle and Buoyant Force

According to Archimedes' Principle, the buoyant force ($\text{F}_\text{B}$) acting on a submerged or floating body is equal to the weight of the fluid displaced by the body. This force always acts vertically upwards.

• When a body is partially or fully immersed in a fluid, it displaces a certain volume of that fluid.
• The weight of this displaced fluid is what determines the magnitude of the buoyant force.

Point of Application of Buoyant Force

The buoyant force acts through a specific point known as the center of buoyancy (denoted as 'B'). This center of buoyancy is always located at the centroid of the volume of the fluid displaced by the body.

• For a floating body, only a part of its volume is submerged, and thus it displaces a volume of fluid equal to the volume of its submerged part.
• The buoyant force acts upwards through the geometric center (centroid) of this displaced volume.

Analyzing the Options for Buoyant Force

Let's examine each given option in the context of the buoyant force acting on a floating body:

1. Centre of gravity of the body: This is the point (G) where the entire weight of the body is considered to act downwards. The buoyant force does not pass through the center of gravity of the whole body, unless the body is entirely submerged and perfectly homogeneous with the fluid.
2. Centre of gravity of the submerged part of the body: While the submerged part of the body occupies the volume that displaces fluid, the buoyant force acts through the centroid of the *volume* of the displaced fluid, which is a geometric property of the displaced space, not necessarily the center of gravity of the material comprising the submerged part. If the body is homogeneous, the center of gravity of the submerged part would coincide with the centroid of the displaced volume, but the most precise definition for the point of action of buoyant force is the centroid of the displaced volume.
3. Metacentre of the body: The metacentre (M) is a point related to the stability of a floating body. It is the point of intersection of the line of action of the buoyant force when the body is tilted through a small angle with the original line of action of the buoyant force. It is not the point through which the buoyant force acts.
4. Centroid of the volume displaced by the body: This is the correct answer. The buoyant force acts through the centroid of the volume of fluid that the body displaces. This point is also commonly referred to as the center of buoyancy. For a floating body, this is the centroid of the submerged volume of the body, as this is the volume that displaces the fluid.

Conclusion on Buoyant Force Location

Therefore, for a floating body, the buoyant force always passes through the centroid of the volume displaced by the body. This point is critical for understanding the stability and equilibrium of floating objects.