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A magnetized needle of magnetic moments  4.8×10−2 Am2   is placed at 300  with the direction of a uniform magnetic field of  3×10−2T. If the needle is pivoted through its center of mass and is free to rotate in the plane of the magnetic field. Find the angular frequency (in rad/s) for small oscillations. The moment of inertia of the needle about the axis of rotation is 2.25×10-5kgm2

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Detailed Solution

Time Period for small oscillations is ,               T=2πIMBH⇒2πT=MBHI ⇒ω=MBHIGiven             M=4.8X10-2Am2BH=3×10-2TI=2.25×10-5Kgm2∴ω=4.8×10-2×3×10-22.25×10-5ω=8rad/sec
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A magnetized needle of magnetic moments  4.8×10−2 Am2   is placed at 300  with the direction of a uniform magnetic field of  3×10−2T. If the needle is pivoted through its center of mass and is free to rotate in the plane of the magnetic field. Find the angular frequency (in rad/s) for small oscillations. The moment of inertia of the needle about the axis of rotation is 2.25×10-5kgm2