A cylinder is rolling without slipping along a roller coaster. It starts at height h above the ground with an unknown initial velocity of v_0. It travels downwards to ground level, goes around a vertical loop of unknown radius R with its base at ground level, before climbing a hill of height 5/3h. At the top of the hilll the cylinder comes to a stop. Find v_0 and the maximum possible value for R such that the cylinder doesnot fall at the top of the loop.