A smooth sphere of radius R is made to translate line with a constant acceleration a=g. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of angle θ as it slides down.

Explanation

The situation is shown in figure. As the sphere is accelerating, it becomes a non-inertial frame for the particle and when particle is displaced, pseudo force acting on it will also do work in addition to gravity and will cause increment in its kinetic energy.
Using work-energy theorem at points A and B, we have
`0+mgR(1-costheta)+maRsintheta=1/2mv^2`
or `v=sqrt(R{a sin theta+g(1-costheta)])`