In this system moment of inertia of the whole system about the axis shown in the question is given ( sphere is able to freely rotate about its axis)
"i want to know why we are not treating sphere as a point mass? why are we considering its rotation about its own axis and adding its moment of inertia *as all the points of the sphere are moving in the same way around the axis * .i am not able to see any rotational motion of sphere about its axis so why are we considering its moment of inertia about its axis
But according to me Moment of inertia of this system should be like this. treating sphere as point mass located at L+R distance from the axis of rotation