A cylindrical cork, of length $\displaystyle l$ and radius $\displaystyle r$, slowly extracted from the neck of a bottle. If the normal pressure per unit of area between the bottle and the unextracted part of the cork at any instant is constant and is equal to P, show that the work done in extracting it is $\displaystyle \pi \mu rl^2P$, where $\displaystyle \mu$ is the coefficient of friction.