दो द्रव्यमानविहीन स्प्रिंगें जिनका स्प्रिंग नियतांक \(2 k\) तथा \(9k\) है, उनके मुक्त सिरों पर \(50\,g\) तथा \(100\,g\) द्रव्यमान बंधे है। दोनों द्रव्यमान इस प्रकार उर्ध्वाधर दोलन करते है कि उनका अधिकतम वेग समान है। उनके संगत आयामों का अनुपात ज्ञात कीजिए।

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.