R मीटर त्रिज्या तथा M किलोग्राम द्रव्यमान की एक वृत्ताकार चकती डिस्क के लंबवत अक्ष के परितः घूर्णन कर रही है। डिस्क पर एक बाह्य बल आघूर्ण इस प्रकार लगाया जाता है कि \(\theta(t)=5 t^2-8 t\), जहाँ \(\theta(t)\) घूर्णन करती चकती की समय \(t\) के फलन के रूप में कोणीय स्थिति है। जब \(t=2 s\) हो, तो आरोपित बल आघूर्ण द्वारा कितनी शक्ति प्रदान की जाती है?

A \(72 MR ^2\)
B \(8 MR ^2\)
C \(108 MR ^2\)
D \(60 MR ^2\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(60 MR ^2\)

Step-by-step Solution

Detailed explanation

\(\theta =5 t ^2-8 t \) \( \omega =\frac{ d \theta}{ dt }=10 t -8 \) \( \alpha =\frac{ d \omega}{ dt }=10 \) \( \therefore p =\tau \omega \) \( =( I \alpha) \omega \) \( =\left(\frac{ mR ^2}{2}\right) \alpha \omega \) \( =\left(\frac{ mR ^2}{2}\right)(10)(10\) \(t =2\) रखने पर…

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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