A mass m moves with speed v0 in a circle of radius r0 on a frictionless tabletop. The mass is attached to a string that passes through a hole in the table at the center of the circle. The string is slowly pulled downward until the particle is moving in a circle with radius rf from the hole.
(A) Find the mass's final velocity in terms of r0, rf, and v0.
(B) Find the tension in the string when the mass is moving in a circle of radius r in terms of m, r, and the angular momentum L.
(C) Calculate the work done on the particle by the tension force T by integrating T · dl. Express your result in terms of r and L.