Problem 1.260

A uniform solid cylinder $A$ of mass $m_{1}$ can freely rotate about a horizontal axis fixed to a mount $B$ of mass $m_{2}$ (Fig. 1.66). A constant horizontal force $F$ is applied to the end $K$ of a light thread tightly wound on the cylinder. The friction between the mount and the supporting horizontal plane is assumed to be absent. Find: (a) the acceleration of the point $K$; (b) the kinetic. energy of this system $t$ seconds after the beginning of motion.