A shown in the figure, a liquid is at same levels in two arms of a U-tube of uniform cross-section when at rest. If the \(U\)-tube moves with an acceleration ' \(f\) ' towards right, the difference between liwuid height between two arms of the \(\mathrm{U}\)-tube will be, (acceleration due to gravity \(=\mathrm{g}\) )

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.