  In this paper we study the dynamics of a small rigid body in a viscous
incompressible fluid in dimension two and three. More precisely we investigate
the trajectory of the rigid body in the limit when the its mass and its size
tend to zero. We show that the velocity of the center of mass of the rigid body
coincides with the background fluid velocity in the limit. We are able to
consider the case where the density of the small rigid body is uniformly
bounded respect to its size.
