(i)[4]
If the forces exerted on $S$ by the base and the sloping side of the bowl have the same magnitude, calculate the speed of $S$.
(ii)[3]
If instead $S$ is just about to lose contact with one of the surfaces, determine the angular speed of $S$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A sphere $S$ of mass $m\,\mathrm{kg}$ is inside a smooth hollow bowl with a vertical axis and a sloping face that makes an angle of $60^\circ$ to the horizontal. $S$ travels at constant speed round a horizontal circle of radius $0.6\,\mathrm{m}$ (see Fig. 1). $S$ touches both the flat base and the sloping side of the bowl (see Fig. 2).