Three identical conducting balls A, B and C, each of mass m, are thrown upward at an angle \(\Theta\) to the horizontal with an initial speed \(v\) in a region of space that has a uniform electric field \(E\) downward along with the gravitational field \(g\). A is positively charged, B is uncharged and C is negatively charged. Rank the ranges R of these three balls in increasing order.

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.