Two identical uniform solid spheres, each of mass 5 kg and radius 10 cm , are connected by a uniform thin rod of mass 3 kg and length 20 cm . The ends of the rod are attached to the surfaces of the spheres such that the centers of the spheres and the rod lie on a single straight line. The system is rotated about an axis passing through the center of the rod and perpendicular to it. If the angular acceleration of the

Step-by-step solution

Let the axis of rotation be passing through the center of the rod. Distance of the center of each sphere from the axis of rotation, d = L 2 + R = 20 2 + 10 = 20 cm = 0.2 m . Moment of inertia of the rod about the axis, I_ rod = 1 12 M_ r L^2 = 1 12 3 (0.2)^2 = 0.01 kg m ^2 . Moment of inertia of one solid sphere about the axis of rotation (using parallel axis theorem), I_ sphere = 2 5 M_ s R^2 + M_ s d^2 = 2 5 5 (0.1)^2 + 5 (0.2)^2 = 0.02 + 0.20 = 0.22 kg m ^2 . Total moment of inertia of the system, I = I_ rod + 2