The area of cross-section of a large tank is \(0.5 \; m ^{2}\). It has a narrow opening near the bottom having area of cross-section \(1 \; cm ^{2}\). A load of \(25 \; kg\) is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is \(40 \; cm\) above the bottom, will be \(\dots \; cms ^{-1}\). \(\left[\right.\) Take \(\left.g =10 \; ms ^{-2}\right]\)

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.