A uniform rod of mass M and length L is hinged at its lower end on a table. The rod can rotate freely in vertical plane and there is no friction at the hinge. A ball of mass M and radius `R = (L)/(3)` is placed in contact with the vertical rod and a horizontal force F is applied at the upper end of the rod.
(a) Find the acceleration of the ball immediately after the force starts acting.

(b) Find the horizontal component of hinge force acting on the rod immediately after force F starts acting.

Answer

(a) `(3F)/(4M)`
(b) `(7F)/(8)`