But why is it obviously 4 ? Is it equally obvious that if the small disk was rolling around the inside of the large disk then the answer would be 2 ?
If you already know the relationship between distance traveled by the center of the small circle and number of rotations, then of course both answers (for outside of circle, or inside) are obvious, but the inside case doesn't seem intuitive.
btw, it seems they were intending "3" to be the right answer, but the wording isn't even close to what it'd have to be for that to be the right answer!
The way I think of it, is if the outer circle is just sliding with friction such that the same point of the little circle is in contact with the big circle, it would undergo a single full rotation. Or is you slid a box along the surface of the drum, it would naturally undergo a single rotation. So then when add in the "rolling", you get the 3.
If you already know the relationship between distance traveled by the center of the small circle and number of rotations, then of course both answers (for outside of circle, or inside) are obvious, but the inside case doesn't seem intuitive.
btw, it seems they were intending "3" to be the right answer, but the wording isn't even close to what it'd have to be for that to be the right answer!