The top of a smooth inclined plane of length \(20 \sqrt{2} \mathrm{~m}\) is connected to the edge of a well of diameter \(40 \mathrm{~m}\) making an angle \(45^{\circ}\) as shown in figure. A body is projected along the inclined plane with a velocity ' \(u\) '. If the body crosses the well without falling in it then the minimum value of ' \(\mathrm{u}\) ' is \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

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.