The speed of a $$4$$-pole induction motor is controlled by varying the supply frequency while maintaining the ratio of supply voltage to supply frequency $$(V/f)$$ constant. At rated frequency of $$50$$ $$Hz$$ and rated voltage of $$400$$ $$V$$ its speed is $$1440$$ $$rpm$$. Find the speed at $$30$$ $$Hz,$$ if the load torque is constant

A $$3$$ phase, $$4$$ pole, $$400$$ $$V,$$ $$50$$ $$Hz,$$ star connected induction motor has following circuit parameters $${r_1} = 1.0\Omega ,\,{r_2} = 0.5\Omega ,$$ $${\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {x_1} = x{'_2} = 1.2\Omega ,{\mkern 1mu} {x_m} = 35\Omega $$
The starting torque when the motor is started direct-on-line is (use approximate equivalent circuit model)

Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,

A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full load slip is 4%, the ratio of the starting developed torque to the full load torque is approximately equal to