Calculate the moment of inertia of An 8.00-kg cylinder, of length 19.5cm and diameter 12.0 cm,about the central axis of the cylinder,if the cylinder is (1) thin-walled and hollow, and (2)solid

The moment of inertia of a body doesn''t change if we don''t change the distance of particles from axis. So, moment of inertia of a cylinder about central axis is same as moment intertia about same axis of a disc/ring(if hollow).

For ring, 

I=Mr²

For disc,

I=(Mr²)/2

You can put the values.

 It is a formua based ..

(1) For hollow cylinder - as we know that for a ring moment of inertia is MR²  .. so a hollow cylinder is also a type of collection of rings.. so therefore its moment of inertia is MR²

(2) For solid cylinder - we can resemble it with that of collection of discs. i.e. MR²/2 ..

and we can similarly also see that moment of inertia of cylinder does not depends on its length..