The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius 2 R rotating anti-clockwise with angular speed $\omega / 2$. The ring and disc are separated b frictionaless ball bearings. The system is in the x-z plane. The point $P$ on the inner disc is at distance $R$ from the origin, where OP makes an angle of $30^{\circ}$ with the horizontal. Then with respect to the horizontal surface,
Select ALL correct options:
A
the point O has linear velocity $3 \mathrm{R} \omega \hat{\mathrm{i}}$.
B
the point $P$ has a linear velocity $\frac{11}{4} R \omega_{\hat{i}}+\frac{\sqrt{3}}{4} R \omega \hat{k}$
C
the point $P$ has linear velocity $\frac{13}{4} R w_{\hat{i}}-\frac{\sqrt{3}}{4} R \omega_{\hat{k}}$
D
The point $P$ has a linear velocity $\left(3-\frac{\sqrt{3}}{4}\right) R w_{\hat{i}}+\frac{1}{4} R w_{\hat{k}}$.
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