Hold your ground.

A small body A is fixed to the inner side of a thin rigid hoop of radius R and mass equal to that of the body A. The hoop rolls without slipping over a horizontal plane. At the moments when the body A gets into the lower position, the centre of the hoop moves with velocity VoV_{o} . The maximum value of VoV_{o} at which the hoop moves without bouncing is xgR\sqrt{xgR}. What is the value of x'x'?

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