A $3$ phase, $415$ V$,50$ Hz$,8$ pole, squirrel cage induction motor is running at $725$ rpm$.$

The power input at this speed is $35$ kW$.$ Stator losses are $0\mathrm{.}65$ kW and the friction and

windage losses are $0\mathrm{.}4$ kW$.$

$($i$)$ When do the following value of slip occur

$$ s $=0$

$$ s $=1$

$$ s $<0$

$($ii$)$ Calculate the slip and the power delivered to the rotor, Pgap.

$($iii$)$ Calculate the mechanical power developed and hence determine the rotor

losses.

$($iv$)$ Calculate the efficiency of the machine.