The center of mass is a fundamental concept in physics and engineering that refers to the point at which the mass of an object is concentrated. For a composite body, which is made up of multiple individual bodies or components, the center of mass can be determined using the principle of weighted averages. In this case, the correct answer is option 'D', which states that the center of mass for the composite body is the ratio of the product of centroid and mass to the total mass.

Explanation:

1. Understanding the center of mass:
- The center of mass is the point at which an object can be balanced, meaning that if this point is supported, the object will remain in equilibrium.
- It is often represented by the symbol 'CM' and is a crucial concept in various fields of study, including physics, engineering, and biomechanics.

2. Composite body and centroid:
- A composite body is formed by combining multiple bodies or components together.
- The centroid of a body refers to the geometric center or average position of its constituent points.
- The centroid is a significant property of a body, as it helps determine its stability, balance, and other mechanical properties.

3. Determining the center of mass for a composite body:
- To find the center of mass for a composite body, the individual masses and their respective centroids must be considered.
- The center of mass is determined using a weighted average, where the mass of each component is multiplied by its centroid and then divided by the total mass of the composite body.
- Mathematically, the center of mass (CM) can be expressed as:
CM = (m1*x1 + m2*x2 + m3*x3 + ... + mn*xn) / (m1 + m2 + m3 + ... + mn)
where m1, m2, m3, ..., mn are the masses of the individual components, and x1, x2, x3, ..., xn are their respective centroids.

4. The correct answer:
- Option 'D' states that the center of mass for the composite body is the ratio of the product of the centroid and mass to the total mass.
- This is consistent with the weighted average approach described above, where the product of each component's mass and centroid is divided by the total mass of the composite body to determine the center of mass.

In conclusion, the center of mass for a composite body is determined by considering the masses and centroids of its individual components. The correct answer, option 'D', correctly states that the center of mass is the ratio of the product of the centroid and mass to the total mass. This principle is crucial in various applications, such as structural analysis, mechanical design, and motion dynamics.

The point at which the total area of a plane figure is assumed to be concentrated is called a