A reel, consisting of a spindle of radius c with two circular ends of radius a, is placed on a rough inclined plane and has a thread wound on it which unwinds when the reel rolls downwards. If \mu is the coefficient of friction and \alpha the inclination of the plane to the horizontal, show that the reel can be drawn up the plane by means of the thread if \mu be not less than \frac{c\sin a}{a - c\cos a}.