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

Options

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

Answer

To solve the problem, we need to determine the distance of the center of mass (COM) of a body where all particles are situated at a distance \( R \) from the origin.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- All particles of the body are located at a distance \( R \) from the origin. This means they are positioned on the circumference of a circle with radius \( R \).

2. **Definition of Center of Mass**:
- The center of mass of a system of particles is defined as the point where the weighted relative position of the distributed mass sums to zero. Mathematically, it can be represented as:
\[ \text{COM} = \frac{\sum m_i \vec{r_i}}{\sum m_i} \]
where \( m_i \) is the mass of the \( i^{th} \) particle and \( \vec{r_i} \) is its position vector.

3. **Position of Particles**:
- In this case, since all particles are at the same distance \( R \) from the origin, we can assume their positions are distributed evenly around the circle.

4. **Symmetry Consideration**:
- Due to the symmetry of the arrangement (all particles are equidistant from the origin), the center of mass will also lie along the same axis as the particles, but it will not be outside the circle.

5. **Distance of COM from Origin**:
- Since the particles are all at distance \( R \), the center of mass can either be at the origin (if the mass distribution is symmetric and uniform) or at a point along the radius \( R \) but cannot exceed \( R \). Therefore, the distance of the center of mass from the origin must be less than or equal to \( R \).

6. **Conclusion**:
- The distance of the center of mass of the body from the origin is:
\[ \text{Distance from origin} \leq R \]

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