The phase equivalent circuit parameters for a $3-$phase, $50$ Hz $,$ delta connected, $6-$pole, squirrel cage induction motor are provided in the table below.

When supplied from a variable frequency $\backslash$& variable voltage supply the induction motor drives a constant torque load at variable speed.

$($i$)$ Sketch the induction motor torque speed curve and show where a constant load torque curve would be located. Explain how the induction motor is controlled to produce the constant load torque at variable speed.

$($ii$)$ If the rated slip at $50$ Hz is $0\mathrm{.}07,$ determine the corresponding load torque that this motor can supply.

$($ii$)$ Calculate the new phase voltage and frequency supplied to the machine in order to supply this constant load torque at $0\mathrm{.}6$ times the rated speed at $50$ Hz $.$

$($iii$)$ Calculate the motor torque when the supply frequency is reduced to $10$ Hz $.$ Comment on your answer.