Reduced mass:

When there is no external force acting on a system of two particles and the only forces are those of mutual interaction, then the system behaves as a single particle of mass.

Let us consider a system of two particles \( m_1 \) and \( m_2 \) having position vector \( r_1 \) and \( r_2 \) respectively with respect to the origin O as shown in the Fig. 1.

Then the reduced mass of this system of two particles is

\( \displaystyle{\mu=\frac{m_1m_2}{m_1+m_2}} \)

• It acts as a point which is known as centre of mass.
• This point divide the line joining the two masses in the inverse ratio of masses.