$6\mathrm{.}1$ A $3,$ four$$pole$,50$Hz Induction Motor $($I$.$M$.)$ runs at $1460$rpm Find its percentage slip.

$6\mathrm{.}2$ A two$$pole$,50$Hz induction motor runs at $2890$rpm$.$ Calculate $($i$)$ Synchronous speed of the motor, and $($ii$)$ slip of the motor.

$6\mathrm{.}4$ A four$$pole induction motor has stator frequency of $50$Hz and rotor frequency of $2$Hz$.$ Calculate the speed at which motor is running and the slip.

$6\mathrm{.}5$ A $3,$ four$$pole induction motor is supplied from $350$Hz$$AC supply. Find:

synchronous speed

rotor speed when slip is $4\%$

the rotor frequency when runs at $600$rpm

$6\mathrm{.}7$ A $12$ pole $3$ alternator is coupled to an engine running at $500$rpm If supplied a $3$ induction motor having full speed of $1440$rpm Find the percentage slip, frequency of rotor current and number of poles of rotor.

$6\mathrm{.}16$ A four$$pole $50$Hz $3$ induction motor running at full load, develops a torque of $160$N$$m$,$ when a rotor makes $120$ complete cycles per minute, find out power output.

$6\mathrm{.}18$ A $50$Hz$,3,$ eight$$pole induction motor takes $46$kW at $720$rpm$.$ The stator Cu$$loss is $1\mathrm{.}2$kW$,$ stator core loss is $1\mathrm{.}4$kW$,$ and rotor mechanical losses are $1$kW$.$ Find the motor efficiency.

$6\mathrm{.}19$ The power input to a $500$V $50$Hz$,$ six$$pole$,3$ squirrel case inductor motor running at $975$rpm is $40$kW$.$ The stator losses are $1$kW and friction and windage losses are $2$kW$.$

Find:

Slip

Rotor Cu loss

Brake hp