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So I have been having a bit of trouble trying to derive the moment of inertia of a solid sphere through its center of mass. Here is my working as shown in the attached file.

The problem is, I end up getting a solution of I = (3/5)MR^2, whereas, in any textbook, it says that the inertia should be equal to I = (2/5)MR^2. Is anyone able to tell me where I went wrong in my working? This is not a homework problem by the way.

Thanks.

The problem is, I end up getting a solution of I = (3/5)MR^2, whereas, in any textbook, it says that the inertia should be equal to I = (2/5)MR^2. Is anyone able to tell me where I went wrong in my working? This is not a homework problem by the way.

Thanks.