The figure shows a solid sphere $($center at point $P,$ radius $R=22\mathrm{.}0cm$ and mass $m_1=12\mathrm{.}0kg)$ which connected with a soliD rod $($length$,AB=L=1\mathrm{.}8m$ mass $m_2=8\mathrm{.}0kg.$ A force $(F)$ applied at point B$.$ Combined object $($system$)$ Keeps at rest by force F$,$ but it has Freedom to rotate around point $P.$

a$)$ Draw a free body diagram for the conbined object.

b$)$ Find an algebraic for total moment of inertia for the system $($solid sphere thod$)$

C$)$ Find an algebraic equation for force $F$ by assuming the system is at rest