एक ठोस बेलन, जिसको दो द्रव्यमानरहित रस्सियों के द्वारा सममित रूप से चित्रानुसार लटकाया गया है। रस्सियों को खोलने पर, यदि यह बेलन गिरता है, तो अपनी आरम्भिक स्थिर स्थिति के सापेक्ष \(cm\) दूरी के बाद यह \(4\,ms ^{-1}\) की चाल प्राप्त कर लेगा। (यदि \(g =10\,ms ^{-2}\) )

A \(60\)
B \(30\)
C \(120\)
D \(150\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(120\)

Step-by-step Solution

Detailed explanation

From energy conservation \(mgh =\frac{1}{2} m v^{2}+\frac{1}{2} I ^{2}\) \(mgh =\frac{1}{2} mv ^{2}+\frac{1}{2} \frac{ mR ^{2}}{2} \omega^{2}\) \(10\,h =\frac{16}{2}+\frac{16}{4} \Rightarrow h =1.2\,m =120\,cm\)

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.

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