Two bar magnets A and B are geometrically similar but the magnetic moment of A is twice that of B . T₁ is the time period of oscillation when their like poles are kept together. When unlike poles are kept together, the time period of oscillation is T ₂ . The ratio T ₁: T ₂ will be

Step-by-step solution

Magnetic moments and inertia: Let M_A and M_B be the magnetic moments, with M_A = 2M_B . Given geometric similarity, moments of inertia are equal: I_A = I_B = I . The period of oscillation in uniform field B is T = 2 I_ net M_ net B . Combined moment of inertia is I_ net = 2I . Like poles: Net magnetic moment adds: M_ net1 = M_A + M_B = 3M_B . Period is T₁ = 2 2I 3M_B B . Unlike poles: Net magnetic moment subtracts: M_ net2 = M_A - M_B = M_B . Period is T₂ = 2 2I M_B B . The ratio is T₁ T₂ = M_B B / 2I 3M_B B / 2I