JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Magnetic Properties of Matter

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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) $8 : 3$ ✓ Correct
(C) $1 : 3$
(D) $27 : 16$

Answer: (B)

Solution

The time period of oscillation of a bar magnet is

T = 2 π \frac{I}{M B _{H}}

. Taking the ratio:

\frac{T _{1}}{T _{2}} = \frac{I _{1}}{I _{2}} \times \frac{M _{2}}{M _{1}}

. Given

\frac{T _{1}}{T _{2}} = \frac{3}{4}

and

\frac{I _{1}}{I _{2}} = \frac{3}{2}

, we have

\frac{9}{16} = \frac{3}{2} \times \frac{M _{2}}{M _{1}}

. Solving:

\frac{M _{2}}{M _{1}} = \frac{9}{16} \times \frac{2}{3} = \frac{3}{8}

, so

\frac{M _{1}}{M _{2}} = \frac{8}{3}

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Magnetic Properties of Matter

Solution

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