A small spherical ball of radius \(0.1 \,mm\) and density \(10^{4} \,kg m ^{-3}\) falls freely under gravity through a a distance \(h\) before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of \(h\) wil be \(m\). (Given \(g =10 \,ms ^{-2}\), viscosity of water \(=1.0 \times 10^{-5} \,N - sm ^{-2}\) )

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.