I found this puzzle from an old issue of a science magazine জ্ঞান ও বিজ্ঞান ("Knowledge and Science")(August, 1977); submitted by Amal Dash, a teacher of Scottish Church school, Kolkata; as mentioned in the magazine.
Incidentally; the answer wasn't published there.
The original publication did not contained any sketch. I've added a few to make it easily readable.
A wheel has an outer radius r1 and an inner radius r2. The wheel is rolling on a floor.
Normally, r1 > r2.
Before the wheel was being rolled, the topmost (from ground) point of outer margin (dot A) and inner margin (dot B) was marked with color dots.
After rolling; the wheel was stopped in a situation, when the 2 colored dots came upwards. So, in the mean-path; the wheel turned complete (integer) turns.
Since the both circles on the wheel revolved n-complete turns; then point A (on big circle) should have been shifted 2nπr1 and similarly the point B (on small circle) should have been shifted 2nπr2.
But if so; since we can see after complete turns the point A and B came to similar orientation as initial, and so dots A and B shows same shift from their own initial positions in horizontal direction; so 2nπr1 should be = 2nπr2; ie. r1 = r2 . And we know very well that r1 ≠ r2.
So, where lies the fallacy? what was going inside the circle?