A yo-yo is made of three disks, as shown : two outer disks of mass M = 40 g, radius R = 3.0 cm, and thickness d = 1.2 cm, sandwiched around an inner disk of mass m = 20 g, radius r = 1.5 cm, and the same thickness d = 1.2 cm. A string is wrapped around the inner disk. The free end is attached to a ceiling, and then the yo-yo is released from rest.

a) What is the tension in the string as the yo-yo falls? What fraction of the yo-yo's weight is this?

b) What is the yo-yo's linear speed when it has fallen a distance of H = 0.5 m? How does this compare to what the speed would be if it fell with no string attached?

R m M M