A string wrapped around a hub of radius R pulls with force FT on an object that rolls with...

A string wrapped around a hub of radius R pulls with force FT on an object that rolls without slipping along horizontal rails on "wheels" of radius r<R. Assume a mass m and rotational inertia I. (a) Prove that the ratio of FT to the object's acceleration is negative. (Note: This object can't roll without slipping unless there is friction.) You can do this by actually calculating the acceleration from the translational and rotational second laws of motion, but it is possible to answer this part without such a "real" calculation, (b) Verify that FT times the speed at which the suing moves in the direction of FT (i.e., the power delivered by FT) equals the rate at which the translational and rotational kinetic energies increase. That is, FT does all the work in this system, while the "internal" force does none, (c) Briefly discuss how parts (a) and (b) correspond to behaviors when an external electric field is applied to a semiconductor,