A horizontal $800$ N merry$-$go$-$round of radius $1\mathrm{.}50$ m is initially at rest. A

group of people pushing on the outer edge produces a constant tangential

acceleration of $1\mathrm{.}10$ m$/$s$2$ at the edge. Consider the merry$-$go$-$round to be a

solid cylinder in determining its moment of inertia.

$($a$)$ Find the kinetic energy of the merry$-$go$-$round after $3\mathrm{.}00$ s$.($b$)$ How long must

the tangential acceleration be sustained if the rotational kinetic energy is to be

$350$ J$?$