A lighter object can fall faster: terminal velocity in the Stokes regime

Abstract We show that, under specific conditions, a lighter object can reach a higher terminal velocity than a heavier one when falling through a highly dense and viscous fluid. This counterintuitive result, obtained within the regime where Stokes’ law applies, challenges the common assumption that heavier objects fall faster. While it is well known that compact objects fall at similar rates in air regardless of mass, and that heavier objects typically fall faster when lighter ones are more extended, the behavior in denser and more viscous media has been less explored. We analyze spheres with different densities and radii falling in such a medium, considering gravitational, buoyant, and drag forces, and assuming no interaction between them. Depending on the radius ratio, the denser sphere may reach a higher terminal velocity and touch the ground first—whether it is heavier, lighter, or equal in weight to the other. Interestingly, when the less dense sphere has the higher terminal velocity, it is always the heavier one; however, whether it lands first also depends on the initial height. These findings provide new insights into low-Reynolds-number dynamics, with potential applications in education, experimental design, and engineering.