The centre of mass of two particles lies:

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(C) The centre of mass $(CM)$ of a system of two particles with masses $m_1$ and $m_2$ located at positions $\vec{r}_1$ and $\vec{r}_2$ is given by th

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on the line joining the particles

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(C) The centre of mass $(CM)$ of a system of two particles with masses $m_1$ and $m_2$ located at positions $\vec{r}_1$ and $\vec{r}_2$ is given by the formula:$\vec{R}_{CM} = \frac{m_1\vec{r}_1 + m_2\vec{r}_2}{m_1 + m_2}$This formula represents a weighted average of the position vectors of the two particles.Since $\vec{R}_{CM}$ is a linear combination of $\vec{r}_1$ and $\vec{r}_2$,the position vector of the centre of mass must lie on the straight line segment connecting the two particles.Therefore,the centre of mass always lies on the line joining the two particles.

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