Magnetic Effects & Magnetism

JEE Main level, single correct, medium

248 of 276

Question 248 of 276

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3s3s and 4s4srespectively. If their moments of inertia are in the ratio of 3:23:2 then the ratio of their magnetic moments will be

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Answer: (B) 8:38:3

Torque on a bar magnet kept in a magnetic field is given by τ=MBsin⁡θ\tau =MB\sin \theta.
Hence, for small oscillations the time period of bar magnets is given by,
T=2πIMB⇒M∝IT2T=2\pi \sqrt{\dfrac{I}{MB}}\Rightarrow M\propto \dfrac{I}{{T}^{2}}
⇒M1M2=I1I2×(T2T1)2\Rightarrow \dfrac{{M}_{1}}{{M}_{2}}=\dfrac{{I}_{1}}{{I}_{2}}\times {\left(\dfrac{{T}_{2}}{{T}_{1}}\right)}^{2}
⇒M1M2=32×(43)2=83\Rightarrow \dfrac{{M}_{1}}{{M}_{2}}=\dfrac{3}{2}\times {\left(\dfrac{4}{3}\right)}^{2}=\dfrac{8}{3}

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