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,

Options

A. The point `O` has a linear velocity `3Romegahati`
B. The point `P` has a linear velocity `11/4 Romegahati+(sqrt(3))/4Romegahatk`
C. The point `P` has a linear velocity `13/4Romegahati+(sqrt(3))/4Romegahatk`
D. The point `P` has a linear velocity `(3-(sqrt(3))/4)Romegahati+1/4Romegahatk`

Answer

A, B

Explanation

`vecV_0=3omega Rhati`

`vecV_(P)=(3omegaR-(omegaR)/2cos60^@)hati+(omegaR)/2sin60hatj`
`(11omegaR)/4hati+(sqrt(3)omegaR)/4hati`