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Q.3. A freely suspended magnet oscillates with period T in earth 's horizontal magnetic field. When a bar magnet is brought near it, such that the magnetic field created by bar magnet is in same direction as earth 's horizontal magnetic field, the period decreases to T 2 . The ratio of the field of the magnet F to the earth's magnetic field (H) is
(a) 1 : 3
(b) 1 : 1
(c) 3 : 1
(d) 9 : 1

Dear Student,


restoring torque due to the field T=-MBsinθfor theta very smallsinθθT=-MBθT=Iαα=-MBθIcompare with α=-ω2θω=MBIT=12πIMBlet the horizontal earth magnetic field be B and that of the external magnet be B'T=12πIMBT2=12πIMB+B'14πIMB=12πIMB+B'14.1B=1B+B'B+B'=4BB'B=4-1=3so the ratio is 3:1Regards

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