A light string is wound many times round a uniform solid cylinder of mass $m$. The free end of the string is tied to the ceiling, and the cylinder is released from rest with the string vertical, as shown in the figure. As the cylinder falls, the string unwinds without slipping. The acceleration of the cylinder and the tension in the string are

Fig. 1: A solid cylinder of mass m hanging from the ceiling by a string wound round it, falling with acceleration a as the string unwinds.