Springer Mechanics problem.

A uniform solid cone (height $h = 4m$ , $\alpha = 30^o$ ) is inclined against a vertical axis as shown in the figure. The cone rotates about its own axis as well as rotates about the vertical axis with angular speeds marked in the diagram. If the cone does not slip at point $B$

find $\large\ \frac { { \omega }_{ 1 } }{ { \omega }_{ 2 } }$