A

three phase, $480$ V$,50$ hp induction motor is supplied $70$ A at a $08$ lagging power factor Its stator and rotor

copper losses are $425753$ and $1000$ W$,$ respectively Its core losses are $3000$ W$,$ the friction and windage

losses are $800$ W$,$ and the stray losses are $200$ W Determine the following

$($a$)$

The air gap power

$($b$)$

The mechanical power developed

$($c$)$

The shaft output power

$($d$)$

The efficiency of the motor