A playground merry$-$go$-$round has a radius of $3\mathrm{.}0.$m and a rotational inertia of $600$ kg m$\text{'}.$ It is initially spinning at $0\mathrm{.}80$ rad$/$s when a $20-$kg child crawls from the center to the rim. When the child reaches the rim and rotates together with the merry$-$go$-$round, the total kinetic energy of the merry$-$go$-$round and the child is:$($a$)150$ J$($b$)208$J$($c$)250$ J$($d$)309$ J$($e$)472$ J