Two balls with masses M and m are connected by a rigid rod of length L and negligible mass as in Figure P10.22. For an axis of rotation perpendicular to the rod, show that the system has the minimum moment of inertia when the axis passes through the center of mass. Show that this moment of inertia is I = L2, where = Mm/(m+M)
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This is a very basic and important question of rigid body mechanics.
Any body has minimum moment of inertia about it's center of mass. This is a basic rule of moment of inertia, which has been derived here by calculas method.
The solution is given with explanation.