A $440$ V$,3-$phase, star connected, $4$ pole, $50$ Hz induction motor has following parameters R$1=0\mathrm{.}05$ ohms, R$2\text{'}=0\mathrm{.}09$ ohms, X$1=$ X$20\mathrm{.}35$ ohms. The motor is driven by $3-$phase voltage source inserter $($VSl$)$ maintaining the ratio vif constant The motor drives a load having torque T$1=0\mathrm{.}009$ omega$^3,$ N$-$m$.$ where omega, is rotor speed in rad $/$ sec$.$ Determine operating speed and torque at $50$ Hz $($Ans: $1476$ rpm$.214\mathrm{.}14$ Nm$)$