A $3-$phase, $6$ pole induction motor is rated $400$Hz$,150$V$,10$hp$,3\%$ slip at rated power output. The

rotational losses are $200$W at rated speed. With the motor operating at rated voltage, frequency, slip, and

output power. Determine:

a$)$ Rotor speed.

b$)$ Frequency of the rotor current.

c$)$ Power crossing the air gap.

d$)$ Rotor copper loss.

e$)$ Output torque.