$35\mathrm{.}4$

A man stands on a platform that is rotating $($without friction$)$ with an initial rotational kinetic energy $K_1=80$ J$.$ His arms are outstretched and he holds a heavy weight in each hand. The rotational inertia of man, weights and platform about the central, vertical axis is $I_1=5\mathrm{.}0kg{m}^2.$ If$,$ by moving the weights, the man decreases the rotational inertia of the system to $I_2=3\mathrm{.}5kg{m}^2,$ what is the final angular speed of ${}_2?$

$($A$)7\mathrm{.}6ra\frac{d}{s}$

$($B$)9\mathrm{.}3ra\frac{d}{s}$

$($C$)5\mathrm{.}4ra\frac{d}{s}$

$($D$)6\mathrm{.}2ra\frac{d}{s}$

$($E$)8\mathrm{.}1ra\frac{d}{s}$