What is the position vector of centre of mass of the two particle system?

For two particle system, the position vector of centre of mass of the two particle system is given by,

$$\vec{r} = \frac {m_1 \vec{r_1} + m_2 \vec{r_2}}{m_1+m_2}$$

For two particle system, velocity of centre of mass is given by,

$$\vec{v_c} = \frac {m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1+m_2}$$

Whewe,

\(m_1\) and \(m_2\) are the masses of two particles.

\(\vec{r_1}\) and \(\vec{r_2}\) are the position vector of the particles \(m_1\) and \(m_2\) respectively.

\(\vec{v_1}\) and \(\vec{v_2}\) are velocities of the particles \(m_1\) and \(m_2\) respectively.