Twp Point Masses m1 and m2 are joined by a weightless rod of length r. Calculate the moment of inertia of the system about an axis passing through the center of mass and perpendicular to the rod.

Ans: (m1m2r^2)/(m1+m2)

Dear Nehal Wani

Center of mass of the system from mass m1  =  (m1*0 + m2*r)/(m1+m2)

                                                                 = m₂ r/(m1+m2)

distance of COM from the mas m2  = [r- m₂ r/(m1+m2)] 

                                                  =m₁ r/(m1+m2)

moment of inertia I = m1 [m₂ r/(m1+m2)]² + m1[m₁ r/(m1+m2)]²

                             =m₁ m2 r²/(m1+m2)

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