$($a$)$ A $26\mathrm{.}0$kg child is riding a playground marry go round that is rotating at $40\mathrm{.}0$ rev$/$min$.$ what centripetal force is exerted if he is $1\mathrm{.}25$m from its center? $($b$)$ What centripetal force is exerted if the merry$-$go$-$round rotates at $4\mathrm{.}00$ rev$/$min and he is $9\mathrm{.}00$m from its center?