A light rod of length `L` is hinged to a plank of mass m. The plank is lying on the edge of a horizontal table such that the rod can swing freely in the vertical plane without any hindrance from the table. A particle of mass `m` is attached to the end of the rod and system is released from `theta = 0^(@)` position (see figure)

(a) Assume that friction between the plank and the table is large enough to prevent it from slipping and calculate the smallest normal force applied by the plank on the table.
(b) Assume that friction is absent everywhere and calculate the speed of the plank when the rod makes `theta = 180^(@)`.

Answer

(a) `(2mg)/(3)`
(b) ` 2 sqrt(gL)`