electromagnetism - Faraday's paradox

I have studied that Faraday's law of induction and motional emf are two different lines of thinking but are essentially same.

But then, how can Faraday's paradox be explained by Faraday's law of induction? Particularly in paradoxes in which Faraday's law of induction predicts zero EMF but there is a non-zero . The wikipedia article is more confusing rather than enlightening.

I need an explanation regarding the article regarding this picture

EDIT : I wanted to know how is flux changing if faraday's law is valid .