 Solution

Substitution givesRotational symmetry about the translation axis forbids a transverse force. Linearity of the Stokes equations and boundary conditions makes the force linear in $U$; dissipation makes the force on the translating sphere oppose its motion. Thus the drag is axial and proportional to $U$, without computing the stress integral. Dimensional analysis further gives scale $\mu aU$; the exact single-sphere coefficient is $6\pi$.