KCET 2025 Physics Paper

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