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 o given by the equation m cos³ 0 – (M + m)(3 cos 0 − 2 cos α) = 0.

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 o given by the equation m cos³ 0 – (M + m)(3 cos 0 − 2 cos α) = 0.