Q.Define centre of mass. Write down its mathematical form. Two particles of masses 2g and 3g are situated at the positions (2 cm, 3 cm) and (4 cm, 5 cm) respectively. Find the position vector of the centre of mass of the two particles.

The centre of mass (c.m.) is the single hypothetical point at which the entire mass of an extended, finite-sized object (or system of objects) can be treated as concentrated, allowing Newton's laws of motion -- which strictly apply only to point masses -- to be validly applied to real, extended objects. For a system of n particles, its position is the mass-weighted average of the individual particles' positions, $\vec{r}=\frac{\sum m_i\vec{r_i}}{M}$ (or the corresponding integral, $\vec{r}=\frac{\int \vec{r}\,dm}{M}$, for a continuous mass distribution); its velocity and acceleration are similarly the mass-weighted averages of the individual particles' velocities and accelerations. …