AIIMS 2018 Physics Viscosity and Stokes' Law MCQ Question

The value of $h$ can be derived from the balance of forces acting on the ball when it reaches terminal velocity in water, where the gravitational force $(mg)$ is equal to the drag force $(6\pi \eta r v)$. Given that the density of the ball $\rho$ and the density of water $\rho_{H_2O}$ are involved, we find that $h$ is proportional to $r^4$ and inversely proportional to the viscosity $\eta$, leading to the expression $h = \frac{2}{81} r^4 \left( \rho - \frac{1}{\eta} \right)^2 g$, which corresponds to option C.

Options A and B incorrectly relate the radius $r$ and viscosity $\eta$ in their formulations, while option D misrepresents the relationship by incorrectly squaring the term involving viscosity, leading to incorrect dimensions and values.