Problem $8$: A $3-$phase induction motor is being driven at $95$ Hz and has $8$ poles. Initially, the motor is

connected to a mechanical load that requires $12$ Nm of torque while spinning at a speed of $1100$ rpm$.$ Assume

rotational losses are negligible.

a$)$ What is the slip? $(3$ points$)$

b$)$ What is the power supplied to the load? $(3$ points$)$

c$)$ If a new load with different torque is connected that requires half as much power, what is the new speed

of the motor in rpm and slip assuming that the motor is operating in its normal operating range? $(14$

points$)$