question_answer 10)

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be  where M is the mass of the sphere and R is the radius of the sphere.                                           [Central Schools 11] (b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be  find its moment of inertia about an axis normal to the disc and passing through a point on its edge.  

Answer:

(a) Here The tangent EF is parallel to the diameter CD.         By the theorem of parallel axes,     Fig. 7.103     . (b) By the theorem of parallel axes, M.I. about an axis passing through an edge point and normal to disc = M.I. about central normal axis .