Buoyancy Force: Line of Action on Floating Bodies

An object floating in a liquid experiences an upward force known as the buoyancy force. This force counteracts the object's weight and is determined by Archimedes' principle, stating it equals the weight of the fluid displaced.

Buoyancy Force Defined

The buoyancy force is the upward push exerted by a fluid that opposes the weight of an immersed or floating object. Its magnitude is equivalent to the weight of the fluid displaced by the object.

Line of Action Location

The line of action for the buoyancy force is the imaginary vertical line passing through the point where the resultant buoyant force acts. This specific point is referred to as the center of buoyancy.

Center of Buoyancy Explained

The center of buoyancy is geometrically defined as the centroid (the geometric center) of the volume of the fluid displaced by the floating body. It is the point through which the total buoyant force is considered to act.

Floating Body Options Analysis

Understanding the options helps clarify where the buoyancy force acts:

• Centre of mass of the floating body: This point represents where the entire weight of the body acts. It's crucial for stability calculations but not the point of action for buoyancy.
• Centre of gravity of the floating body: Similar to the center of mass, this relates to the body's weight distribution and is not the location of the buoyant force.
• Centroid of the displaced volume: This is the geometric center of the submerged part of the object, which corresponds to the volume of fluid pushed aside. The buoyancy force acts through this point.
• Lowest point of the displaced volume: This specific location does not correspond to the resultant action point of the buoyancy force.

Buoyancy Force Acting Point

Consequently, for any floating body, the vertical line of action of the buoyancy force passes through the centroid of the displaced volume.