The centre of mass is the ratio of the product of centroid and mass to the total mass. This can be explained in detail as follows:

1. Understanding the Centre of Mass:
- The centre of mass is a point in an object or system that represents the average position of all the mass.
- It is the point where the object or system can be balanced, as if all the mass is concentrated at that point.
- The centre of mass is a crucial concept in physics and engineering, as it helps in analyzing the motion and stability of objects.

2. Definition of Centroid:
- The centroid is a geometric property of a shape or object.
- It represents the average position of all the points in the shape or object.
- In simpler terms, it is the point at which a shape or object would balance if it were placed on a pin.

3. Relationship between Centre of Mass and Centroid:
- The centre of mass and centroid are related to each other, but they are not the same thing.
- For simple and regular objects with uniform mass distribution, the centre of mass and centroid coincide.
- However, for irregular objects or objects with non-uniform mass distribution, the centre of mass and centroid may not coincide.

4. Calculation of Centre of Mass:
- To calculate the centre of mass of an object or system, we need to consider the mass and position of each individual component.
- The centre of mass is calculated by taking the sum of the products of the mass and position of each component, divided by the total mass of the object or system.
- Mathematically, the centre of mass (CM) can be represented as CM = (m1r1 + m2r2 + m3r3 + ... + mnrn) / (m1 + m2 + m3 + ... + mn), where m represents the mass of each component and r represents the position vector of each component.

5. Relationship to the Total Mass:
- The centre of mass is a ratio of the product of centroid and mass to the total mass.
- This means that the position of the centre of mass is influenced by both the mass of each component and its position relative to the centroid.
- The total mass of the object or system is taken into account to determine the overall distribution of mass and its effect on the centre of mass.

Overall, the correct answer is option D, which states that the centre of mass is the ratio of the product of centroid and mass to the total mass. This relationship helps in understanding and calculating the position of the centre of mass in objects or systems with non-uniform mass distribution.