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CBSE Class 11-science Answered

How will you prove that the centre of mass of two particles divides the line joining the particles in the inverse ratio of their masses?
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Let us consider a two particle system of masses m1 and m2 at the points A and B respectively.

Consider point C as the centre of mass of system. If  and  are the position vector of masses m1 and m2, the position of the centre of mass will be given as-
If the origin of co-ordinate system is shifted at the centre of mass C of the system, then
.
 Using eq. (1) we get
 
Hence, the centre of mass of two particle system divides the line joining the particles in the inverse ratio of their masses.
Answered by | 04 Jun, 2014, 03:23: PM
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