A grinding circuit is processing $810$ t$/$h $($of dry feed$),$ using $38$kWh$/$t to reduce the circuit feed of $80\%$ passing $2,400$um$,$ to the circuit product of $80\%$ passing $160$um$.$

a$)$ How much energy is the mill drawing at the pinion?

b$)$ How much will the work index change when the required circuit product of $80\%$ passing is $90$um$?$