Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3: 2, then the ratio of their magnetic moments will be: (a) 2: 1 (b) 8: 3 (c) 1: 3 (d) 27: 16

Answer: (b). T = 2π√(I/MBH) ⇒ M ∝ I/T² (M₁)/(M₂) = (I₁)/(I₂)·(T₂²)/(T₁²) = 3/2 × 16/9 = 8/3 So the answer is (b) 8: 3.

Two bar magnets oscillate in a horizontal plane in earth's magnetic… | JEE Main 2022 (27 Jul, Shift 1)

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Vibration Magnetometer

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $3\text{ s}$ and $4\text{ s}$ respectively. If their moments of inertia are in the ratio of $3 : 2$ , then the ratio of their magnetic moments will be:

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Answer: (b)

$T = 2\pi\sqrt{\frac{I}{MB_H}} \Rightarrow M \propto \frac{I}{T^2}$
$\frac{M_1}{M_2} = \frac{I_1}{I_2}\cdot\frac{T_2^2}{T_1^2} = \frac{3}{2} \times \frac{16}{9} = \frac{8}{3}$
So the answer is (b) 8 : 3.

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