$(12)$ Imagine that you apply a $($net$)$ torque of $12$ N m to speed up the rotation of a solid sphere about its central axis, from an initial $20\mathrm{.}0ra\frac{d}{s}$ to $100ra\frac{d}{s}$ in a time of $5\mathrm{.}0$ s $.$ To achieve the same kinematic result, what torque would you need to apply if you used a sphere $[$of a different material$]$ that had an equal mass but only $\frac{2}{3}$ of the radius of the original sphere?