A particle of mass m is kept on the top of a smooth sphere of radius R.

A particle of mass $m$ is kept on the top of a smooth sphere of radius $R$. It is given a sharp impulse which imparts it a horizontal speed v. (a) Find the normal force between the sphere and the particle just after the impulse. (b) What should be the minimum value of $v$ for which the particle does not slip on the sphere? (c) Assuming the velocity $v$ to be half the minimum calculated in part, (b) Find the angle made by the radius through the particle with the vertical when it leaves the sphere.