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Q. Two identical particles are located at $\vec{x}$ and $\vec{y}$ with reference to the origin of three dimensional co-ordinate system. The position vector of centre of mass of the system is given by

System of Particles and Rotational Motion

Solution:

$\vec{r}=\frac{m_1 \vec{r}_1+m_2 \vec{r}_2}{m_1+m_2}=\frac{m(\vec{x}+\vec{y})}{2 m}=\frac{\vec{x}+\vec{y}}{2}$.