The moment of inertia of a uniform circular disc of mass M and radius R about its diameter is `(1)/(4) MR^(2)` . What is the moment of inertia of the disc about an axis passing through its centre and perpendicular to the plane of the disc?

Explanation

If we consider another diameter on the plane of the disc perpendicular to the diameter mentioned in the question, the moment of inertia of the disc will also be `(1)/(4)MR^(2)`. The intersection point of these two diameters is the centre of the disc, so the moment of inertia of the disc about an axis passing through its centre and perpendicular to the plane of the disc (according to te perpendicular axis theorem),
` I = (1)/(4) MR^(2) + (1)/(4)MR^(2) = (1)/(2)MR^(2)`