A $2\mathrm{.}00-$kg sphere is rotating about an axis through its center at $40\mathrm{.}0$ rev$/$s with the angular velocity in the $+$z$$direction$.$ A torque $10\mathrm{.}0$ N$$m acts on the sphere about the center of the sphere in the $+$x direction. What is the rate of change of the angular momentum of the sphere?

Group of answer choices

$-20\mathrm{.}0$ kg$$m $2/$s $2$

$10\mathrm{.}0$ kg$$m $2/$s $2$

$80\mathrm{.}0$ kg$$m $2/$s $2$

$8\mathrm{.}00$ kg$$m $2/$s $2$

$20\mathrm{.}0$ kg$$m $2/$s $2$