Two identical uniform solid spheres, each of mass M and radius R , have their centres connected by a light rigid rod of length 2R . The radius of gyration of this combined system about an axis passing through the centre of the rod and perpendicular to its length is:

Step-by-step solution

The axis of rotation passes through the centre of the rod of length 2R . The distance from this axis to the centre of each sphere is R . The moment of inertia of one solid sphere about its own diametric axis is I_ cm = 2 5 M R^2 . Using the parallel axis theorem, the moment of inertia of one sphere about the given axis of rotation is: I_ sphere = I_ cm + M d^2 = 2 5 M R^2 + M R^2 = 7 5 M R^2 Since there are two identical spheres, the total moment of inertia of the system is: I_ system = 2 7 5 M R^2 = 14 5 M R^2 The