Question

Two rings of the same radius amd mass are olaced such that their centers are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an acis passing theough the center amd perpendicular to the olane of one the rings is ( mass of the ring = m, radius =r)

a) 1/2mr²

b) mr^{​​​​​2}

c) 3/2 mr^{​​​​​2}

d) 2mr²

Answer 1

The moment of Inertia of such a system would be (3/2)MR² .

The moment of Inertia of the system = The moment of Inertia of Ring rotating about an axis perpendicular to its plane + The moment of Inertia of Ring rotating about an axis in its own plane.

The moment of Inertia of Ring rotating about an axis perpendicular to its plane= MR²

The moment of Inertia of Ring rotating about an axis in its own plane.= MR²/2

So the moment of inertia of the system is

(3/2)MR²