A $250-$V $11-$hp$,4-$pole, $50-Hz,-$connected induction motor has a full$-$load slip of $4\mathrm{.}5\%$ :

$($a$)$ What is the synchronous speed of this motor?

$($b$)$ What is the rotor speed of this motor at the rated load?

$($c$)$ What is the rotor frequency of this motor at the rated load?

$($d$)$ What is the shaft torque of this motor at the rated load?

$($e$)$ Suppose the synchronous speed and rotor speed are $950$ rpm and $900$ rpm $,$ respectively. What is the slip of this motor in this case?