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A hemisphere, of mass M is free to slide with its base on a
smooth horizontal table. A particle of mass m is placed on the hemisphere at an
angular distance a from the vertex; show that the radius to the point of contact
at which the particle leaves the surface, makes with the vertical an angle ✪
given by the equation m cos³ 0 − (M + m)(3 cos 0 − 2 cos a) = 0.

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