$7$ The motorized drum turns clockwise at constant speed, causing the vertical cable to have a constant downward velocity $v.$ As part of the design of this system, determine the tension $T$ in the cable in terms of the $y-$coordinate of the cylinder of mass $m.$ Neglect the diameter and mass of the small pulleys.

Ans. $T=\frac{m}{2y}\sqrt[\phantom{2}]{b^2+y^2}(g+\frac{b^2{v}^2}{4y^3})$