A uniform solid cone (height h, semi–vertex angle $α$ ) 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, then

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$\frac{ω_{1}}{ω_{2}} = 1$

$\frac{ω_{1}}{ω_{2}} = \sqrt{3}$

Velocity of $C = h ω_{1} \sin 2 α$

Velocity of $C = h ω_{1}$

answer is A, C.

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Detailed Solution

Line joining vertex of cone to B will be IAOR

$ω = 2 ω_{1} \cos α V_{C} = 2 ω_{1} \cos α h \sin α = (h \sin 2 α) ω_{1}$

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