The position of centre of mass of system of particles at any moment does not depend on.

Options

A. masses of the particles
B. internal forces on the particles
C. position of the particles
D. relative distance between the particles

Explanation

To solve the question about the position of the center of mass of a system of particles and what it does not depend on, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Center of Mass**:
The center of mass (COM) of a system of particles is a point that represents the average position of the mass distribution in the system. It is calculated using the formula:
\[ \vec{R}_{\text{cm}} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + m_3 \vec{r}_3 + \ldots + m_n \vec{r}_n}{m_1 + m_2 + m_3 + \ldots + m_n} \]
where \( m_i \) is the mass of the \( i^{th} \) particle and \( \vec{r}_i \) is its position vector.

2. **Analyzing the Dependencies**:
- **Masses of the Particles**: The position of the center of mass depends on the masses of the particles, as seen in the numerator of the COM formula.
- **Position of the Particles**: The position vectors \( \vec{r}_i \) also directly influence the center of mass, as they are part of the calculation.
- **Relative Distance Between the Particles**: The relative distances between particles affect the position of the center of mass since they determine how the masses are distributed in space.
- **Internal Forces on the Particles**: Internal forces (forces that particles exert on each other) do not affect the position of the center of mass. The center of mass is determined solely by the masses and their positions, not by the forces acting between them.

3. **Conclusion**:
Based on the analysis above, we can conclude that the position of the center of mass does not depend on the internal forces acting on the particles. Therefore, the correct answer to the question is that the position of the center of mass does not depend on **internal forces on the particles**.

### Final Answer:
The position of the center of mass of a system of particles does not depend on **internal forces on the particles**.

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