A bar magnet has a magnetic moment equal to 5 × 10 - 5 Wb m . It is suspended in a magnetic field which has a magnetic induction B = 8 π × 10 − 4 T . The magnet vibrates with a period of vibration equal to 15 s . The moment of inertia of magnet is

Question

A bar magnet has a magnetic moment equal to 5 × 10 - 5 Wb m . It is suspended in a magnetic field which has a magnetic induction B = 8 π × 10 − 4 T . The magnet vibrates with a period of vibration equal to 15 s . The moment of inertia of magnet is, 4.54 × 10 4 k g m 2, 4.54 × 10 − 5 kg m 2, 4.54 × 10 − 4 kg m 2, 4.54 × 10 5 kg m 2

MARKS App · Accepted Answer

Here, magnetic moment is given in weber-meter, which is the unit of μ 0 M . ∴ μ 0 M = 5 × 10 - 5 Wb-m M = 5 × 10 - 5 μ 0 A m 2 Also, B = 8 π × 10 - 4 = μ 0 H ∴ H = 8 π × 10 - 4 μ 0 T = 2 π I M H I = M H T 2 4 π 2 = 5 × 10 - 5 × 8 π × 10 - 4 × 15 2 4 π 2 μ 0 2 = 5 × 10 - 5 × 8 π × 10 - 4 × 225 4 π 2 4 π × 10 - 7 2 I = 2250 × 10 - 9 π ( 16 π 2 ) × 10 - 14 = 4.54 × 10 5 k g m 2

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