Two narrow bores of diameter \(5.0\, {mm}\) and \(8.0\, {mm}\) are joined together to form a \(U-\)shaped tube open at both ends. If this \({U}\)-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water \({T}=7.3 \times 10^{-2} \, {Nm}^{-1}\), angle of contact \(=0, {g}=10\, {ms}^{-2}\) and density of water \(\left.=1.0 \times 10^{3} \,{kg} \,{m}^{-3}\right]\) (in \(mm\))

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.