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Q.

A right circular cone of base radius R and half apex angle $α$ precesses about a vertical axis passing through it’s apex P such that it’s slant length is making angle $θ$ with vertical as shown in the figure. It is spinning about its own axis with angular velocity $ω_{s}$ . There is no slipping at the point of contact of cone and horizontal surface. At the instant shown A is a point on cone which is in contact with ground and B is diametrically opposite point on it’s base. C is centre of base circle. At this instant:

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a

Speed of point C on cone is $ω_{s} Rsin (θ+α) . \frac{cosα}{sinθ}$

b

Speed of point B on cone is $2 ω_{s} Rsin (θ+α) . \frac{cosα}{sinθ}$

c

Speed of point C on cone is $\frac{ω_{s} Rsin (θ+α)}{\sin θ}$

d

Speed of point B on cone is $\frac{2 ω_{s} Rsin (θ+α)}{\sin θ}$

answer is A, C.

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A right circular cone of base radius R and half apex angle α precesses about a vertical axis passing through it’s apex P such that it’s slant length is making angle θ with vertical as shown in the figure. It is spinning about its own axis with angular velocity ωs. There is no slipping at the point of contact of cone and horizontal surface. At the instant shown A is a point on cone which is in contact with ground and B is diametrically opposite point on it’s base. C is centre of base circle. At this instant: