For a certain engine having an average speed of \(1200 \mathrm{rpm}\), a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within \(2 \%\) above the average speed. The fluctuation of kinetic energy per cycle is found to be \(2 \mathrm{~kg} \cdot \mathrm{m}\). What is the least possible mass of the flywheel if its diameter is not to exceed \(1 \mathrm{~m}\) ?

(a) \(40 \mathrm{~kg}\)

(b) \(51 \mathrm{~kg}\)

(c) \(62 \mathrm{~kg}\)

(d) \(73 \mathrm{~kg}\)