The rotor speed in a three phase induction motor is less than input frequency why?

i am sorry to say that the answer to this question is different,  as follows

In an Ac induction motor The rotor which is rotating is because of the induced magnetic potential in the rotor just like a secondary winding in transformer so when rotor gets the speed of the applied frequncy no magnetic flux is cut therefore the rotor stops rotating. again when it is stopping the filed flux get cut by the rotor which produced current in the rotor winding (squirrel cage) which in turn produced magnetic filed,again the rotor gains the speed so, at one stage it is always lagging .with speed thas the reason the rotor speed always would be2880 rpm, while the applied frqency is3000 rpm

This is due to a drag coefficient. The induced voltage that causes rotation will also create losses. The losses are the cause of the reduced speed.