A circular coil has moment of inertia \(0.8 \,kg m ^{2}\) around any diameter and is carrying current to roduce a magnetic moment of \(20\, Am ^{2}\). The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of \(4\, T\) is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by \(60^{\circ}\) will be

A \(10\, rad \,s ^{-1}\)
B \(20\, \pi \operatorname{rad}\, s^{-1}\)
C \(10\, \pi\, rad\, s ^{-1}\)
D \(20\, rad\, s ^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(10\, rad \,s ^{-1}\)

Step-by-step Solution

Detailed explanation

\(I _{ dia }=0.8 kg / m ^{2}\) \(M =20 Am ^{2}\) \(U _{ i }+ K _{ i }= U _{ f }+ K _{ f }\) \(0+0=- MB \cos 30^{\circ}+\frac{1}{2} I \omega^{2}\) \(20 \times 4 \times \frac{\sqrt{3}}{2}=\frac{1}{2}(0.8) \omega^{2}\) \(\omega=\sqrt{100 \sqrt{3}}=10(3)^{1 / 4}\)

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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