Question

Moment of inertia of hollow cylinder about its perpendicular axis

Answer 1

Moment of Inertia of a hollow cylinder about it's perpendicular axis will be MR^2 where M is the mass of the cylinder and R is the radius of the cylinder.

You can remember this result since the hollow cylinder is made up of a lot of rings, so it's moment of Inertia also coincidentally comes out to be MR^2 which is the moment of inertia for a ring.

Now, for a solid cylinder it'd be MR^2/2 just like the disc because also solid cylinder is made up of lot of discs.