Actually 1 very similar sum is done in HCV.....where u drop a ball from a ht. on a system that has 2 balls attachted to the ends of a rod - and the qsn was to find the minimum ht so the system does a complete rotation....What they did was to conserve energy upto the highest point ....in this case it'll obviously be for C....taking into account the angular velocity of the rod (in this case - it'll be the lamina) abt cm....however in this case IC won't help, coz arguments abt IC converts translation + rot into pure rotation...here it is pure rotation....
However I can relate this to that - it won't be much general of course....want it?