A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the center of mass of the system from the origin is

Explanation

To find the distance of the center of mass of a system of particles placed uniformly around the origin at a distance \( R \), we can follow these steps:

### Step 1: Understand the Configuration
We have a large number of particles uniformly distributed around the origin, each at a distance \( R \). This means that if we were to visualize this, the particles would form a circular boundary with radius \( R \).

**Hint:** Visualize the particles as being evenly spread out on the circumference of a circle.

### Step 2: Define the Center of Mass
The center of mass (COM) of a system is the point where the weighted relative position of the distributed mass sums to zero. For a symmetric distribution of mass, the center of mass will be at the center of the distribution.

**Hint:** Recall that for a symmetric distribution, the center of mass lies at the geometric center.

### Step 3: Analyze the Symmetry
Since the particles are uniformly distributed around the origin, the symmetry of the system implies that the contributions of the particles in all directions will cancel each other out. Thus, the center of mass will be at the origin.

**Hint:** Consider how the forces or positions of particles in opposite directions cancel each other out.

### Step 4: Conclusion
Since the center of mass is at the origin, the distance of the center of mass from the origin is \( 0 \).

**Final Answer:** The distance of the center of mass of the system from the origin is \( 0 \).

### Summary of Steps:
1. Visualize the particles around the origin.
2. Define the center of mass.
3. Analyze the symmetry of the distribution.
4. Conclude that the center of mass is at the origin.