# Leaving the Hemisphere

A point particle of mass m sits at rest on top of a frictionless hemisphere of mass M, which rests on a frictionless table, as shown. The particle is given a tiny kick and slides down the hemisphere. At what angle $$\theta$$ (measured from the top of the hemisphere) does the particle lose contact with the hemisphere if the ratio of $$M$$ to $$m$$ is 2?

Clarification: $$m \ne M$$.

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