All the particles of a body situated at distance `R` from the origin. The distance of the center of mass of the body from the origin is

Options

A. `=R`
B. `leR`
C. `gtR`
D. `geR`

Explanation

To find the distance of the center of mass of a body where all particles are situated at a distance \( R \) from the origin, we can follow these steps:

### Solution Steps:

1. **Understanding the Setup**:
- All particles are located at a distance \( R \) from the origin. This implies that they are positioned on the surface of a sphere (or a circle in 2D) with radius \( R \).

2. **Single Particle Case**:
- If there is only one particle at distance \( R \), the center of mass (CM) is simply at the location of that particle. Thus, the distance of the center of mass from the origin is \( R \).

3. **Two Particles Case**:
- If we have two particles, each at a distance \( R \) from the origin, the center of mass will be located at the midpoint of the line segment joining the two particles.
- The distance of the center of mass from the origin will be less than \( R \) because it is a weighted average of their positions.

4. **Three or More Particles**:
- For three particles, the center of mass will be calculated based on the positions of the first two particles and the third particle. The center of mass will still be closer to the origin than \( R \).
- As we keep adding more particles, the center of mass will continue to be influenced by the positions of all particles, and it will always remain closer to the origin than \( R \).

5. **General Conclusion**:
- For any number of particles located at a distance \( R \) from the origin, the center of mass will always be at a distance less than or equal to \( R \) from the origin. Thus, we can conclude that the distance of the center of mass from the origin is \( \leq R \).

### Final Answer:
The distance of the center of mass of the body from the origin is less than or equal to \( R \).