Correct Answer - Option 1 : 500 rpm and 1165 N-m

**Concept:**

Synchronous speed, \({N_s} = \frac{{120f}}{P}\)

For a three-phase motor, power (P) = √3 VI cos ϕ

Torque = Power / angular frequency(ω)

**Calculation:**

Synchronous speed, \({N_s} = \frac{{120 \times 50}}{{12}} = 500\;rpm\)

Power, P = √3 × 400 × 100 × 0.8 = 60966.4 Watt

Torque, \(T = \frac{P}{\omega } = \frac{{60P}}{{2\pi N}} = \frac{{60 \times 60966.4}}{{2\pi \times 500}} = 1164.96\;Nm\)