It wouldn't take off. Doesn't matter of you spin the conveyor belt at the required speed, the wings are not moving relative to the air, so no lift. Now, if you take the wheels of the plane, set it on a conveyor belt that is lets say quarter mile long, and then move the belt at the required speed, the plane would take off. But if the plane, no pun intended, spinning its wheels, no lift.
I hate those questions though. My highschool physics teacher was evil for them. He would do stupid shit as well, like,
"If a squirrel was sliding down a frictionless roof (covered in ice), how much force would he have to throw the nuts it was carrying each each arm to stop himself from sliding." Like, WTF man. I'm taking an exam, none of this crap.
You should have listened to him a little more carefully.....
OT for this thread, but for some fun reading on the subject, try this.