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Centre of Mass of a Two- Particle System

A particle is defined as an object whose mass is finite but whose size and internal structure can be neglected. A collection of particles, interacting with one another is called a system.

Let us consider a two particle system. The line joining the two particles is X-axis.

Let the distances of the two particles be x1 and x2 respectively from origin. Let m1 and m2 be the masses of the particles respectively. The centre of the mass of the system is that point C which is at a distance X from O, where X is given by
X can be regarded as the mass weighted mean of x1 and x2. If the two particles have the same m1 = m2 = m, then
Thus for two particles of equal mass the centre of mass lies exactly midway between them.
If we have n particles of masses m1, m2,...... mn, respectively, along a straight line taken as the x-axis, then by definition the position of the centre of the mass of the system of particles is given by,
Where x1, x2 ...... xn are the distances of the particles from the origin. X is also measured from the same origin.
Interms of position vectors,

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