In case one phase of a three-phase synchronous motor is short-circuited the motor will

A three-phase synchronous motor requires a three-phase supply to operate. If one phase is short-circuited, the motor will not start because there is no current flowing in the short-circuited phase. The motor will not be able to develop a rotating magnetic field and will not start.

Option B is incorrect because the motor will not run at $\frac{2}{3}$ of synchronous speed. The motor will not start at all.

Option C is incorrect because the motor will not run with excessive vibrations. The motor will not start at all.

Option D is incorrect because the motor will take less than the rated load. The motor will not start at all.