Solution to Problem 1:
Keep following SXC Physics Club.
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 θ (measured from the top of the hemisphere) does the particle lose contact with the hemisphere?
Note: Please send the answer to firstname.lastname@example.org. Solutions to the question will be published after a week.