\(30^{\circ}\) નો ડીપ-કોણ ઘરાવતા સ્થાન \(P\) આગળ ચુંબકીય કંપાસની સોય એક મિનીટમાં \(20\) વખત દોલન પામે છે. \(60^{\circ}\) નો ડીપ કોણ ઘરાવતા \(Q\) સ્થાને પ્રતિ મિનીટ દોલનોની સંખ્યા \(10\) થઈ જાય છે. આ બે સ્થાનો આગળ કુલ ચુંબકીય ક્ષેત્રોનો ગુણોત્તર \(\left( B _{ Q }: B _{ P }\right)..........\) થશે.

A \(\sqrt{3}: 4\)
B \(4: \sqrt{3}\)
C \(\sqrt{3}: 2\)
D \(2: \sqrt{3}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{3}: 4\)

Step-by-step Solution

Detailed explanation

\(T =2 \pi \sqrt{\frac{ I }{ B _{ H } M }}\) \(T _{1}=3\,sec =2 \pi \sqrt{\frac{ I }{\left( B _{ p } \cos 30^{\circ}\right) M }}\) \(T _{2}=6\,sec =2 \pi \sqrt{\frac{ I }{\left( B _{ Q } \cos 60^{\circ}\right) M }}\)…

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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