A $230V,60Hz,6-$pole, Y$-$connected three$-$phase induction motor has the following parameters in ohms$/$phase as referred to the stator:

$R_1=12\mathrm{.}5,R_2=28\mathrm{.}6,x_1=21\mathrm{.}3,x_2=13\mathrm{.}6,R_C=4200,$ and $x_m=1800.$ The friction and windage loss is $3\%$ of the power developed. If the motor speed is $1120$ rpm $,$ determine $($a$)$ power input, $($b$)$ the stator Cu$-$loss, $($c$)$ the rotor Cu$-$loss, $($d$)$ the air$-$gap power, $($e$)$ the power developed, $($f$)$ the shaft torque and $($g$)$ efficiency.