The induction motor can’t run at synchronous speed because it is not possible to run the motor without load. Even the motor is at no load, there would be core loss,copper loss and air friction loss.In a nut shell, the motor slip can not be zero in any case. Therefore, running of induction motor at the synchronous speed is hypothetical speed.
Why Induction Motor cannot run at Synchronous Speed?
The rotor current flows if the voltage is induced in the rotor conductor. The production of the rotor voltage is possible if there exist slip between the actual speed of the rotor and the synchronous speed of the motor. If the actual speed of the rotor is equal to the synchronous speed then the rotor conductor will not cut the stator flux and the voltage induced in the rotor is zero and no torque is produced. Without torque, motoring operation is impossible.
Torque developed by induction motor is proportional to the slip. At synchronous speed, slip is zero and hence torque developed by the motor is zero. In case of ideal motor having zero friction and zero losses, and no external load, motor can rotate at synchronous speed, because motor need not develop any torque to sustain rotation. However for practical motor, there will be some friction and other losses, which motor has to overcome by developing some torque. And to develop that torque, motor must have slip. Therefore Motor can not run at synchronous speed, but at slightly lower speed.
This is why an induction motor can not run at synchronous speed.