Two solid spheres of masses M = 4 kg and m = 2 kg, with radii R 20 cm and r = 10 cm, respectively, are attached at either end of a rod of mass m, = 5 kg and length L = 50 cm to form a dumbbell (see Figure 7). Note that the spheres are attached to the ends of the rod (the rod does not penetrate the spheres). %3D %3D M, R ,r m,, L Figure 7: A dumbbell. (a) What is the moment of inertia of the system about its centre of mass? (b) A coordinate system is set up so that the origin is at the centre of mass of the dumbbell, and the x axis is parallel to the rod, with the positive direction from the M to m. A force: F (0.8 N) + (1.0 N) + (1.2 N) is applied to the outer edge of the small mass m (the edge of the sphere opposite of where it meets the rod). If F is the only force applied to the dumbbell, what is the angular acceleration vector of the dumbbell with respect to the coordinate system that is specified? What is its magnitude?