normal reaction
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Hi Vish0001 see the question is asking normal reaction exerted by ground on the entire ring and not the normal reaction on a particle of the ring. now if you consider a particle N(on particle)=dm(g) + dmw^2r (you have taken as mw^2r) = dm(g+w^2r) integrating we get N(on ring)=Mg+ Mw^2r now this N is considered on the centre of ring i.e centre of mass (because we have taken r as constant while integrating) therefore since the centre does not rotate therefore N=Mg Hope you understood
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