A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B₁ and B₂ are respectively the total magnetic field due to the earth at the two places, then the ratio B₁/B₂ is best given by :
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Question

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B₁ and B₂ are respectively the total magnetic field due to the earth at the two places, then the ratio B₁/B₂ is best given by :

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G1 Physics · Accepted Answer

For a vibration magnetometer, frequency f∝√Bₕ=√(B cosδ). Thus (30/40)²=(B₁cos45°)/(B₂cos30°), giving B₁/B₂≈0.69≈0.7. Hence C.