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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