Question

Centre of mass of a two particle system

Answer 1

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

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