The centre of buoyancy refers to the point at which the buoyant force, acting on a submerged or floating body, can be considered to be applied. It is an important concept in fluid mechanics and plays a crucial role in understanding the stability and equilibrium of floating or submerged objects.

Definition of the Centre of Buoyancy:
The centre of buoyancy is defined as the centroid or the centre of mass of the volume of the fluid that is displaced by the immersed or floating body. In simpler terms, it is the point at which the entire buoyant force can be considered to act. The centre of buoyancy is denoted by the symbol 'B'.

Explanation of the Correct Answer:
The correct answer to the given question is option 'D', which states that the centre of buoyancy is the centre of the volume of the displaced fluid. This answer is based on the Archimedes' principle, which states that an object submerged or floating in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object.

When an object is immersed or floating in a fluid, it displaces a certain volume of the fluid. This displaced volume of fluid exerts an upward force on the object, known as the buoyant force. According to Archimedes' principle, this buoyant force is equal to the weight of the displaced fluid.

The centre of buoyancy is the point where this buoyant force can be considered to act. It is the centre of mass of the displaced fluid volume. This means that if the entire buoyant force is applied at this point, the object will be in equilibrium.

Other Options Explained:
a) The centre of gravity of the body: This option is incorrect because the centre of buoyancy and the centre of gravity are generally not the same. The centre of gravity is the point at which the entire weight of the body can be considered to act. It depends on the distribution of mass within the body and is not related to the buoyant force.
b) The point of intersection of the buoyant force and the gravitational force: This option is incorrect because the point of intersection of these forces does not have any significance in determining the centre of buoyancy. The buoyant force and gravitational force act in different directions and have different points of application.
c) The point of intersection of the buoyant force and the centre line of the body: This option is incorrect because the centre of buoyancy is not necessarily located at the centre line of the body. It depends on the shape and distribution of the displaced fluid volume.

In conclusion, the centre of buoyancy is the centre of the volume of the displaced fluid. It is the point at which the entire buoyant force can be considered to act on an immersed or floating body.

The centre of buoyancy is the point at which the buoyant force acts on a submerged or floating object. It is an important concept in fluid mechanics and plays a crucial role in understanding the stability and equilibrium of floating or submerged bodies.

Explanation:
1. Definition of Centre of Buoyancy:
The centre of buoyancy is defined as the centre of the volume of the fluid that is displaced by the object when it is immersed in a fluid. It is the point at which the upward buoyant force on the body is considered to act.

2. Understanding Buoyant Force:
When an object is submerged in a fluid, it experiences an upward force called the buoyant force. The buoyant force is equal to the weight of the fluid displaced by the object. It acts vertically upward through the centre of gravity of the displaced fluid.

3. Relationship between Centre of Buoyancy and Centre of Gravity:
The centre of buoyancy is not the same as the centre of gravity of the body. The centre of gravity is the point at which the weight of the body is considered to act. It depends on the distribution of mass in the body. On the other hand, the centre of buoyancy depends on the shape and volume of the body and the fluid in which it is immersed.

4. Point of Intersection of Buoyant Force and Gravitational Force:
The point of intersection of the buoyant force and the gravitational force is not the centre of buoyancy. The gravitational force acts vertically downward through the centre of gravity of the body, while the buoyant force acts vertically upward through the centre of gravity of the displaced fluid. These forces may intersect, but their intersection point does not necessarily coincide with the centre of buoyancy.

5. Centre of the Volume of the Displaced Fluid:
The correct answer is option 'D' - the centre of the volume of the displaced fluid. This means that the centre of buoyancy is the centroid or geometric centre of the volume of fluid that is displaced by the submerged or floating body. It is the point at which the upward buoyant force on the body is considered to act.

In conclusion, the centre of buoyancy is the centre of the volume of the displaced fluid. It is not the same as the centre of gravity of the body or the point of intersection of the buoyant force and the gravitational force. Understanding the concept of the centre of buoyancy is essential for analyzing the stability and equilibrium of floating or submerged bodies.