A $2$-pole, $50 \mathrm{~Hz}, 3$-phase induction motor supplies power to a certain load at $2970 \: \mathrm{rpm}$ . The torque-speed curve of this machine follows a linear relationship between synchronous speed and $95 \%$ of synchronous speed. Assume mechanical and stray losses to be zero. If the load torque of the motor is doubled, the new operating speed of the motor, in $\mathrm{rpm}$, is
- $2940$
- $2812$
- $2970$
- $2850$
