An induction motor always runs at a speed less than synchronous speed because the rotating magnetic field which is produced in the stator will generate flux in the rotor which will make the rotor to rotate, but due to the lagging of flux current in the rotor with flux current in the stator, the rotor will never reach .

The rotor of an induction motor never runs at synchronous speed, because then the relative speed between the rotating flux and rotor will be zero and hence, torque will be zero.

Induction Motor Operation
An induction motor is a type of AC motor that works on the principle of electromagnetic induction. It consists of two main parts - the stator and the rotor. The stator is the stationary part of the motor that contains the winding, while the rotor is the rotating part.

Synchronous Speed
The synchronous speed of an induction motor is the speed at which the rotating magnetic field produced by the stator winding rotates. It is given by the formula:

Ns = 120f/P

where Ns is the synchronous speed in revolutions per minute (RPM), f is the frequency of the power supply in hertz (Hz), and P is the number of poles in the stator winding.

The synchronous speed represents the theoretical maximum speed at which the motor should run. However, due to the slip between the rotating magnetic field and the rotor, the actual speed of the rotor is always less than the synchronous speed.

Slip and Torque
The slip of an induction motor is defined as the difference between the synchronous speed and the rotor speed, expressed as a percentage. It is given by the formula:

Slip = (Ns - Nr) / Ns * 100

where Nr is the rotor speed in RPM.

When the rotor speed is less than the synchronous speed, the slip is positive. This slip creates a relative speed between the rotating magnetic field and the rotor, which induces an electromotive force (EMF) in the rotor winding. The EMF causes a current to flow in the rotor, which in turn produces a magnetic field that interacts with the rotating magnetic field of the stator.

The interaction between the rotor and stator magnetic fields generates torque in the motor. The torque produced is directly proportional to the relative speed between the two fields. As the relative speed decreases (i.e., when the rotor speed approaches the synchronous speed), the torque decreases.

Zero Relative Speed and Torque
When the rotor speed reaches the synchronous speed, the slip becomes zero. This means that the relative speed between the rotating magnetic field and the rotor is zero. As a result, there is no relative motion between the two fields, and no torque is produced.

In other words, when the rotor runs at synchronous speed, the rotating magnetic field of the stator and the rotor magnetic field are in perfect synchronization, causing them to cancel each other out. This leads to zero torque production.

Conclusion
In summary, the rotor of an induction motor never runs at synchronous speed because at synchronous speed, the relative speed between the rotating flux and the rotor is zero. As a result, there is no relative motion between the two fields, and hence, no torque is produced. Therefore, the correct answer is option 'D' - zero relative speed and torque.