Question

A and B are two particles of masses m1 and m2 and G is the centre of mass of the system. Now AG : GB is

Answer 1

                  (A) m -----------G----------------------- M(B)

Let AG = x

     BG = AB - x

Let the point A be A(0,0) and

      the point B be B(AB,0)

Therefore, position of centre of mass = (m₁x₁ + m₂x₂)/(m₁ + m₂)

                                                                  = (m*0 + M*AB)/(m + M)

                                                                  = (MAB)/(m + M)

Therefor the point G is G[ (MAB)/(m + M) , 0 ]

AG = (MAB)/(m + M)

BG = AB - (MAB)/(m + M)

Therefore, AG : GB = (MAB)/(m+M) : AB - (MAB)/(m + M)

$AG:BG=\frac{MAB}{m + M} :AB-\frac{MAB}{m + M}$

$AG:BG=\frac{MAB}{m + M} : \frac{AB(m+M)-MAB}{m+M}\\ \\AG:BG=MAB : mAB+MAB-MAB\\\\AG:BG = MAB : mAB\\\\AG:BG = M:m$

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