For a certain engine having an average speed of $$1200$$ rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within $$2$$% about the average speed. The fluctuation of kinetic energy per cycle is found to be $$2$$kJ. What is the least possible mass of the flywheel if its diameter is not exceed $$1$$ m?

A flywheel of moment of inertia $$9.8$$ kg m² fluctuates by $$30$$ rpm for a fluctuation in energy of $$1936$$ Jouls. The mean speed of the flywheel is (in rpm)