A $250$ V$,2$ hp$,18$ pole, $85$ Hz$,$ Y connected induction motor has a full load slip of $5$ percent $($N$.$B$.$: The phrase $$at full load$$ is equivalent to $$at rated load$,$ that is when its output power$/$torque are the rated ones$).($N$.$B$.2$: Remember that, in electric machines, the industry convention is that one hp is exactly $746$ watts.$)$a$)$ What is the synchronous speed of the motor, in rps$,$ rpm and rad$/$s$.$ b$)$ What is the rotor speed of this motor at the rated load. c$)$ What is the frequency of rotor currents of this motor at the rated load. d$)$ What is the shaft torque of this motor at the rated load.