A tank of height \(15 \mathrm{~m}\) and cross-section area \(10 \mathrm{~m}^2\) is filled with water. There is a small hole of cross-section area \(a\) which is much smaller than the container, located at a height of \(12 \mathrm{~m}\) from the base of the container. How much force should be applied with a piston at the top level, so that the water coming out of the hole hits the ground at a distance of \(16 \mathrm{~m}\) ? (Take, density of water \(=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) )

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.