A magnet is suspended in the magnetic meridian with an untwisted wire. The upper end of wire is rotated through 180o to deflect the magnet by 30o from magnetic meridian. When this magnet is replaced by another magnet, the upper end of wire is rotated through 270o to deflect the magnet 30o from magnetic meridian. The ratio of magnetic moments of magnets is

Let M1 and M2 be the magnetic moments of magnets and BH the horizontal component of earth's field. We have τ=MBH sinθ. if ϕ is the twist of wire, then τ=Cϕ, C being restoring couple per unit twist of wire⇒ Cϕ= MH sinθHere, ϕ1=180o-30o=150o=150 x π180 radϕ2=270o-30o=240o=240 x π180 radSo, Cϕ1 = M1BH sin θ (For deflection θ=30o of I magnet) Cϕ2 = M2BH sin θ (For deflection θ=30o of II magnet)⇒ϕ1ϕ2=M1M2⇒M1M2=ϕ1ϕ2=150 x π180240 x π180=1524=58⇒M1 : M2=5 : 8