Suppose that a merry$-$go$-$round, which can be approximated as a disk, has no one on it$,$ but it is rotating about a central vertical axis at $0\mathrm{.}2$ revolutions per second. If a $100$kg$100$kg man quickly sits down on the edge of it$,$ what will be its new speed? $($A disk rotating about its middle has a moment of inertia I$=12$mR$2$I$=21$mR$2,$ mass of merry$-$go$-$round $=200$kg$200$kg$,$ radius of merry$-$go$-$round $=6\mathrm{.}0$m$6\mathrm{.}0$m$)$

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$0\mathrm{.}2$rev$/$s$0\mathrm{.}2$rev$/$s

$0\mathrm{.}0667$rev$/$s$0\mathrm{.}0667$rev$/$s

$0\mathrm{.}1$rev$/$s$0\mathrm{.}1$rev$/$s

$0\mathrm{.}4$rev$/$s$0\mathrm{.}4$rev$/$s