A certain application requires power at a frequency of $16.67$ Hz, while the available grid frequency is $50$ Hz. A $3$-phase synchronous motor connected to the $50$ Hz, $3$-phase grid, driving a synchronous generator, is used for this application.
Which one of the following combinations is a suitable choice for the number of poles in the motor and generator, respectively?
- $2,6$
- $6,2$
- $4,6$
- $6,4$
