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The figure shows a system consisting of ...

The figure shows a system consisting of (i) a ring the outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed `omega` and (ii) an inner disc of radius 2R rotating anti clockwise with angular speed `omega//2.` The ring and disc are separted. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of `30^@` with the horizontal. Then with respect to the horizontal surface,

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