A $460$V$,4$ pole, WW$1$ hp$,60$Hz$,$ Y$-$connected three$-$phase induction motor develops its full$-$load induced torque at WW$2$ percent slip when operating at $60$Hz and $460$V$.$ The per$-$phase circuit model impedances of the motor are R$1=$WW$3,$ X$1=$WW$4,$ Xm$=$WW$5$ and X$2=$WW$6.$ Mechanical, core, and stray losses may be neglected in this problem.

WW$1=39\mathrm{.}4554816089,$ WW$2=3\mathrm{.}8,$ WW$3=0\mathrm{.}4,$ WW$4=0\mathrm{.}43,$ WW$5=42,$ WW$6=0\mathrm{.}58.$

$($a$)$ Find the value of the rotor resistance R$2.($b$)$ Find Tmax and its corresponding slip. What is the rotor speed at maximum torque for this motor in rpm$?($c$)$ Find the starting torque of this motor.