Only the drag law (Option C) follows purely from matching dimensions. In fact, if you assume F depends on the viscosity η, radius r and speed v as F∝ηarbνc then dimensional balance - [ML−2]=(ML−1T−1)a⋅Lb⋅(LT−1)c a=1,b=1,c=1 So F=Kηrν where K is a dimensionless constant (in Stokes' solution K=6π ). The other formulas ( A,B,D ) involve specific functional forms or numerical factors that dimensional analysis alone cannot fix.