A vibrations magnetometer consists of two indentical bar magnet placed one over the other that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is `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 second is :

Options

A. `2^(1//4)`
B. `2^(1//2)`
C. `2`
D. `2^(5//4)`

Answer

C

Explanation

Magnetic moment is a vector quatity. If the magnetic moments of the two magnets are M eachh then the net magnetic moment when the magnets are placed perpendicular to each other is
`M_(eff)=sqrt(M^(2)+M^(2))=Msqrt(2)`
and the moment of inertia is 2I.
Thus, `T=2pi sqrt(I/(Msqrt(2H)))`
When one of the magnets is withdrawn, the time
`T'=2pi sqrt(I/(MH))`
`:.(T')/T=sqrt(1/(2^(1//2))` or `T'=T/(2^(1//4))=2^(5//4-1//4=2sec`