B

To find the distance of the center of mass from the origin when all particles are situated at a distance R from the origin, we can use the definition of the center of mass.
Step 1: The center of mass (CM) of a system of particles is given by the formula:
$$ \vec{R}_{CM} = \frac{1}{M} \sum m_i \vec{r}_i $$
where $M$ is the total mass, $m_i$ are the masses of individual particles, and $\vec{r}_i$ are their position vectors.
Step 2: If all particles are at a distance R, their position vectors are of magnitude R. However, the vector nature of position means that the particles are distributed around the origin.
Step 3: The average (or center of mass) position can produce a resultant vector that might be directed toward the origin depending on their configuration. Hence, the distance of the center of mass, $R_{CM}$, must be less than or equal to R, depending on their distribution.
Therefore, we have: $$ \text{Distance of center of mass} \leq R $$
This leads us to the conclusion that the distance of the center of mass from the origin is less than or equal to R, which corresponds to option B.