1. Two solid spheres with masses M and m are connected by a rigid rod of length L and negligible mass as shown in the figure below. The larger sphere of mass M is on the left and the smaller sphere of...

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Extracted text: 1. Two solid spheres with masses M and m are connected by a rigid rod of length L and negligible mass as shown in the figure below. The larger sphere of mass M is on the left and the smaller sphere of mass m is on the right. The pivot is at a distance x to the right of the larger mass and rotates in a counterclockwise direction (when viewed from overhead). The distance between the pivot and the smaller mass is L - x. (a) For an axis perpendicular to the rod, show that the system has the minimum moment of inertia when the axis passes through the center of mass. (b) Show that this moment of inertia is 1 = µL², where u= mM/(m + M).