A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field 2^ 5 / 4 ~s . One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is :

Step-by-step solution

Time period of magnet in vibration magnetometer, T=2 I M H First case, T₁=2 I₁+I₂ M^ H where, M= resultant magnetic moment of two magnets Here, two identical magnets are placed perpendicular to each other. I₁=I₂=I (Let) and M^ = M^2+M^2 =M 2 T₁=2 2 I 2 M H 2^ 5 / 4 =2 2 I 2 M H (i) When one magnet is removed, then time period, T₂=2 I M H ...(ii) On dividing Eq. (i) by Eq. (ii), we get 2^ 5 / 4 T₂ = 2 2 = 2 2^ 5 / 4 T₂ =2^ 1 / 4 T₂= 2^ 5 / 4 2^ 1 / 4 =2 ~s