A $460$ V four$-$pole $75$hp $60$ Hz three$-$phase induction motor develops its full$-$load

induced torque at $3\mathrm{.}5\%$ slip. The per$-$phase circuit model impedances of the motor

are

R$1=0\mathrm{.}058$ XM $=18$

X$1=0\mathrm{.}32$ X$2=0\mathrm{.}386$

Mechanical, core, and stray losses may be neglected in this problem.

a$)$ Find the value of the rotor resistance R$2[3]$

b$)$ Find the pullout torque, slip at pullout torque and rotor speed at pullout torque $[3]$

c$)$ Find the starting torque