Pb$5-$A $\backslash (480-\backslash$mathrm$\{$V$\},60\backslash$mathrm$\{$~Hz$\},50-\backslash$mathrm$\{$hp$\}\backslash ),$ three phase induction motor is drawing $60$ A at $0\mathrm{.}85$ PF lagging. The stator copper losses are $2$ kW $,$ and the rotor copper losses are $700$ W $.$ The friction and windage losses are $600$ W $,$ the core losses are $1800$ W $,$ and the stray losses are negligible. Find the following quantities: $(8$ Marks$)$

$1.$ The air$-$gap power PAG.

$2.$ The power converted Peonv.

$3.$ The output power $\backslash (\backslash$mathrm$\{$P$\}\_\{\backslash$text $\{$out $\}\}\backslash ).$

$4.$ The efficiency of the motor.