after some quick calculations, is the answer (a)?
This is a very good question. Main motive is to just think of ring motion. Coz you must be getting wrong because of wrong axis of rotation. @RAJESH_MISHRA
Is there any alternative method to do?
it may be there, but I don't know any other alternative. i only stick to this basic method. displace the body by some angle or distance then find net restoring acc and equating it to (omega)^2 X or (omega)^2(thita)