Magnetic field due to currentHard

Question

A vibration magnetometer consists of two identcial 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 is 25/4 sec. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is :-

Options

A.21/4
B.21/2
C.2
D.25/4

Solution

Magnetic moment is a vector quantity. If the magnetic moments of the two magnets are M each then, the net magnetic moment when the magnets are placed perpendicular to each other, is
Meff = = M√2
and the moment of inertia is 2I.
Thus, T = 2π
when one of the magnets is withdrawn, the time period is
T′ = 2π
∴    or   T′ = = 2sec

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