Starting from rest, a constant force F = 100 N is applied to the free end of a 50-m cable wrapped around the outer rim of a uniform solid cylinder, similar to the situation shown in Fig. 10.9(a). The cylinder has mass 4.00 kg and diameter 30.0 cm and is free to turn about a fixed, frictionless axle through its center. 

(a) How long does it take to unwrap all the cable, and how fast is the cable moving just as the last bit comes off?

(b) Now suppose that the cylinder is replaced by a uniform hoop, with all other quantities remaining unchanged. In this case, would the answers in part (a) be larger or smaller? Explain.

Figure 10.9(a): 

9.0 N 0.120 m 50 kg