A Solid sphere has mass M and radius R. Its moment of inertia about a parallel axis passing through a point at a distance R/3 from its centre is

Step-by-step solution

The moment of inertia of a solid sphere about an axis passing through its centre is I_ cm = 2 5 MR^2 . Using the parallel axis theorem, the moment of inertia about a parallel axis at a distance d from the centre is given by I = I_ cm + Md^2 . Given d = R 3 , substituting the values: I = 2 5 MR^2 + M ( R 3 )^2 I = 2 5 MR^2 + 1 9 MR^2 I = ( 18 + 5 45 )MR^2 I = 23 45 MR^2 Answer: 23 MR ^2/45