A magnet suspended so as to swing horizontally makes 50 vibrations per minutes at a place where dip is 30∘ , and 40 vibrations where dip is 45∘ . Compare the earth's total fields at the two places.

We know time period of oscillation of magnetic needle   T=2πIMBH                  (∵ Frequency =n=1T) ⇒n ∝ BH ⇒n1n2=BH1cosθ1BH2cosθ2      [Take Horizontal component of field]Given data  n1=50,n2=40,θ1=30°,θ1=45°               ⇒⇒5040=BH1BH2×cos30°cos45°2516=BH1BH232⇒BH1BH2=2586