Recent experimental activities of boson trapping on a ring geometry open the way to explore a novel topology. We focus on a tight ring trap with strong transverse confinement leading to an effectively one-dimensional motion along its circumference. We consider a strongly interacting bose gas on the ring subjected to a localized barrier potential which is suddenly set into motion. The Bose-Fermi mapping allows to obtain an exact solution for the many-body wavefunction in the impenetrable-boson (Tonks-Girardeau) limit of infinitely strong interactions between the particles with arbitrary external potential, not treatable with the Bethe Ansatz. Using the time-dependent extension to BF mapping an exact solution for the dynamical evolution of the many-body wavefunction is obtained. The exact solution allows to calculate the particle current, the particle current fluctuations and the drag force acting on the barrier. In the weak barrier limit the stirring drives the system into a state with net zero current and vanishingly small current fluctuations for velocities smaller than v_c=ħπ/(mL), with m the atomic mass and L the ring circumference. The existence of a velocity threshold for current generation indicates superfluid-like behavior of the mesoscopic Tonks-Girardeau gas, different from the non-superfluid behavior predicted for the TG gas in an infinite tube. At velocities approaching integer multiples of v_c angular momentum can be transferred to the fluid and a nonzero drag force arises. At these velocities we predict the formation of a macroscopic superposition of a rotating and a nonrotating Fermi sphere of the mapped Fermi gas. We calculate the momentum distribution, time of flight images and the Wigner function of the Bose gas, the latter allowing to identify quantum interferences in the superposition. We find that the barrier velocity should be larger than the sound velocity for a better discrimination of the two components of the superposition.
