4.4 ** A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ro with angular velocity wo, but I now pull the string down through the hole until a length remains between the hole and the particle. (a) What is the particle's angular velocity now? (b) Assuming that I pull the string so slowly that we can approximate the particle's path by a circle of slowly shrinking radius, calculate the work I did pulling the string. (c) Compare your answer to part (b) with the particle's gain in kinetic energy.