10 cm ત્રિજ્યાની નક્કર ગોળો તેના કેન્દ્રથી 15 cm દૂર રહેલી અક્ષને અનુલક્ષીને ભ્રમણ કરે છે. આ અક્ષને અનુલક્ષીને ચક્રાવર્તન ત્રિજ્યા બરાબર \(\sqrt{n}\) cm છે. તો n નું મૂલ્ય _______ છે.

A 265
B 100
C 325
D 125

Verified Solution

Answer & Solution

Correct Answer

(A) 265

Step-by-step Solution

Detailed explanation

ધારો કે ભ્રમણ ત્રિજ્યા k છે. \( \Rightarrow mk^{2} = \frac{2}{5} mR^{2} + md^{2}\) \(k^{2} = \frac{2}{3} \times 10^{2} + 15^{2} = 265\) \((\sqrt{n})^{2} = 265 \Rightarrow n = 265\)

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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