A flexible cable is wound in one row round a drum with a radius R. The weight of a unit of cable length is \rho. The entire cable weighs G. The drum moves by inertia without slipping along a horizontal surface, and the cable is wound off it. At the initial moment, when the cable was completely wound on the drum, the velocity of the drum centre was v.

Find the velocity of the drum centre at the moment of time when a part of the cable with a length x lies on the surface, neglecting the radius of the cable cross section(in comparison with R) and the mass of the drum.

For diagram, refer: Drum - Mechanics problem on Flickr - Photo Sharing!

Answer:
Spoiler:
\sqrt{\frac{Gv^2 + \rho gxR}{G - \rho x}}


How to solve it?