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A cone is rolling on a sufficiently rough surface. The cone has a slant height of R, the radius of the base circle is r and during its movement, the cone rotates about its stationary apex with an angular velocity $ω_{y}$ . The cone also rotates about its rotational axis with an angular velocity $ω_{0}$ . What is the angular velocity of any point on the surface of the cone with respect to the immediate axis of rotation?

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$ω = ω_{0} \sqrt{1 - \frac{r^{2}}{R^{2}}}$

$ω = ω_{0} \frac{r}{R} \sqrt{1 - \frac{r^{2}}{R^{2}}}$

$ω = ω_{0} \frac{r}{R}$

$ω = ω_{0} \sqrt{1 + \frac{r^{2}}{R^{2}}}$

answer is D.

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