A pneumatic radial tire includes a carcass, opposing bead portions, a carcass reinforcing ply extending between the bead portions, and opposing bead cores situated within respective opposing bead portions. An annular hollow tube member is situated within a bead portion, the tube member containing within a tube internal passageway a viscous fluid and a plurality of spherical balls within the viscous fluid. The spherical balls are dimensioned and sized to freely move circumferentially about the tube passageway. The balancing bodies operationally reposition within the tube passageway to cancel imbalance effects within a running wheel assembly including the tire. The tube member may be located in a tire apex member or form a tire bead core within the tire bead portion with carcass reinforcing ply endings surrounding the tube member.