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 `3 R omega hat(i)`
B. the point P has a linear velocity `(11)/(4) R omega hat(i) + (sqrt(3))/(4) R omega hat k`
C. the point oP has a linear velocity `(13)/(4) R omega hat(i) - (sqrt(3))/(4) R omega hat (k)`
D. the point P has a linear velocity `(3 - (sqrt(3))/(4))R omega hat (i) + (1)/(4) R omega hat(k)`

Answer

A, B