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