Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Consider the following statements regarding the centre of mass of a system of particles: (A) For two particles of equal mass, the centre of mass lies midway between them. (B) The centre of mass of a system of particles can be located using the relation \( \mathbf{R} = \frac{\sum m_i \mathbf{r}_i}{M} \). (C) The centre of mass of any body must always coincide with its geometric centre, even if the density is non-uniform. (D) If the coordinate system is chosen such that the origin is at the centre of mass, then \( \sum m_i \mathbf{r}_i = 0 \). Choose the correct answer from the options given below:

1. (A) and (C) only
2. (B) and (C) only
3. (A), (B) and (D) only
4. (A), (B), (C) and (D)