# Centre of mass of a two particle system

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Centre of mass of a two particle system

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In figure (a), two particles of masses m1 and m2 are separated by distance d and the origin coincide with the particle of mass m1. The position of the centre of mass (com) of this two particles is given by

$$x_{com}=\frac{m_2}{{m_1}+{m_2}}d$$

In figure (b), In which the co-ordinate system has been shifted leftward. The position of the centre of mass is

$$x_{com}=\frac{{m_1}{x_1}+{m_2}{x_2}}{{m_1}+{m_2}}$$

Similarly for y and z-axis

$$y_{com}=\frac{{m_1}{y_1}+{m_2}{y_2}}{{m_1}+{m_2}}$$ and

$$z_{com}=\frac{{m_1}{z_1}+{m_2}{z_2}}{{m_1}+{m_2}}$$

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