Q$5.[$Total $10$ marks$]$ A thin bar of mass $3$ kg and length $2$ m is suspended from two cables with equal length that are attached at ends A and $B.$ The other ends of the cables are fixed to a frictionless pivot at $P,$ which moves horizontally on the collar with acceleration $a.$

Free body diagram

a$)[3$ marks$]$ Draw the free$-$body diagram $($in the space above$)$ for the bar in the position shown with cable PB vertical.

b$)[5$ marks$]$ Write down the equations of motion of the bar and hence calculate the required acceleration $a$ of the collar that will maintain the bar at the angle shown $($with cable PB vertical$).$

c$)[2$ marks$]$ For the situation in part b$,$ calculate the tension in each cable.