A boy is sitting on an igloo in a hemispherical shape, as shown in the figure. If it starts to slide from rest, neglecting friction, at what height h relative to the horizontal is the point O at which it will lose contact with the hemispherical surface of radius R?

In the figure, the spring is ideal, situation (a) is the stable equilibrium of the spring-mass system, and situation (b) is that of the spring at rest. Releasing block M as indicated in the situation (b), determine:
a) The spring constant;
b) The maximum speed reached by block M.