Two thin bar magnets of equal mass and length have magnetic moments M₁ and M₂ ( M₁ > M₂ ). They are tied together such that their centers coincide and their axes are parallel. When suspended in a uniform magnetic field, the combination has a time period of oscillation of 3 s when their like poles are on the same side, and 6 s when their opposite poles are on the same side. The ratio of their magnetic moments M₁ M₂ is

Step-by-step solution

Let I be the moment of inertia of each magnet. The total moment of inertia of the combination is I_ eq = I + I = 2I in both cases. The time period of oscillation is given by T = 2 I_ eq M_ eq B When like poles are on the same side (sum configuration), the equivalent magnetic moment is M_ eq = M₁ + M₂ . Thus, T₁ = 2 2I (M₁ + M₂)B = 3 s When opposite poles are on the same side (difference configuration), the equivalent magnetic moment is M_ eq = M₁ - M₂ . Thus, T₂ = 2 2I (M₁ - M₂)B = 6 s Taking the ratio of the two t