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^(3//4)`

Answer

C

Explanation

Initially magnetic moment of system
`M_(1)=sqrt(M^(2)+M^(2))=2M` and moment of inertia
`I_(1)=I+I=2I`.
Finally when one of the magnet is removed then
`M_(2)=M` and `I_(2)=I`
So `T=2pisqrt(I/(M B_(H)))`
`T_(1)/T_(2)=sqrt(I_(1)/I_(2)xxM_(1)/M_(2))=sqrt((2I)/IxxM/(sqrt(2)M))`
`implies T_(2)=2^(5//4)/2^(1//4)= 2 sec`.