two particles having masses m1 and m2 are placed at a separation r between them locate the centre of mass - Physics - System Of Particles And Rotational Motion

Question

two particles having masses m1 and m2 are placed at a separation r
between them locate the centre of mass of arrangement show that the
distances of centre of mass from the particles m1 amd m2 are in
ratio m2:m1?

Ved Prakash Lakhera · Accepted Answer

Let C  M
 be at a distance  X from mass m1 in such a way that                      X =m1 r1+m2r2m1+m2                     r2=r-r1So          X =m1 r1+m2r-r1m1+m2We are given     r1r2=m1m2or                    r1=m1m2r2=m1m2r-r1                     r1m1+m2m2=m1ror                  r1 = m1m2rm1+m2Putting this value of r1 in the eqn of C
 M
                   X =m1m1m2rm1+m2+m2r- m1m2rm1+m2m1+m2 =  m12m2+m1m2+m22-m1m22rm1+m22     or                 X=m1m2m1-m2+m2m1+m2m1+m22r

two particles having masses m1 and m2 are placed at a separation r between them.locate the centre of mass of arrangement. show that the distances of centre of mass from the particles m1 amd m2 are in ratio m2:m1?