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Question

A circular coil has moment of inertia 0.8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2. 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, acquired after rotating by 60, will be :

A
10 rad s1
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B
10π rad s1
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C
20π rad s1
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D
20 rad s1
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Solution

The correct option is A 10 rad s1
Given, Moment of inertia of circular coil, I=0.8 kg m2
Magnetic moment of circular coil, M=20 Am2

Rotational kinetic energy of circular coil is,
KE=12Iω2

Here, ω= angular speed of coil.

Potential energy of coil, when considered equivalent to a bar magnet is,

U=MBcosϕ

From energy conservation,

12Iω2=UiUf

12Iω2=MBcos60(MB)

MB2=12Iω2

20×42=12(0.8)ω2

ω=10 rad/s.

Hence, (A) is the correct answer.

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