KCET 2025 Physics Paper

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.