A spherical ball of radius \(1 \times 10^{-4} \mathrm{~m}\) and density \(10^5\) \(\mathrm{kg} / \mathrm{m}^3\) falls freely under gravity through a distance \(h\) before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately _______. (The coefficient of viscosity of water is \(9.8 \times 10^{-6}\) \(\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.