A solid steel sphere of radius $6\mathrm{.}00$ cm and mass $7\mathrm{.}07$ kg is mounted on an axle through its center.

a$.$ How large is the rotational inertia of this sphere, in $kg*m^2?$

b$.$ Starting from rest, what torque $($in $m*N)$ applied to the sphere will cause it to reach an angular speed of $250ra\frac{d}{s}$ in $10\mathrm{.}0$ seconds? $[$Hint: Apply Newton's $2$nd law, for rotation.$]$

c$.$ What force F applied tangentially on the edge of the sphere will produce this acceleration?

d$.$ Once the sphere is spinning at $250ra\frac{d}{s},$ how much kinetic energy of rotation does it have?