Student \(A\) and Student \(B\) used two screw gauges of equal pitch and \(100\) equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is \(0.322\, {cm}\). The absolute value of the difference between the final circular scale readings observed by the students \(A\) and \(B\) is .... . [Figure shows position of reference \('O'\) when jaws of screw gauge are closed] Given pitch \(=0.1 \,{cm}\).

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.