A solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. The ratio of moment of inertia of the sphere about its tangent to the moment of inertia of the disc about a tangent in its plane will be x : y . The value of x and y respectively is

Step-by-step solution

Mass of the solid sphere, M_s = 5 kg Mass of the disc, M_d = 4 kg Let the radius of both the sphere and the disc be R . The moment of inertia of a solid sphere about its tangent is obtained using the parallel axis theorem: I_s = I_ cm + M_s R^2 = 2 5 M_s R^2 + M_s R^2 = 7 5 M_s R^2 Substituting M_s = 5 kg: I_s = 7 5 5 R^2 = 7 R^2 The moment of inertia of a disc about a tangent in its plane is also obtained using the parallel axis theorem (shifting from the diameter): I_d = I_ diameter + M_d R^2 = 1 4 M_d R^2 + M_d