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 time 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

Time period of vibration magnetometer `T=2pisqrt((I)/(MB))`
When two magnets are placed perpendicular to each other, `M^(1)=sqrt(M^(2)+M^(2))=sqrt2m`
`T_(1)=2pisqrt((2I)/(sqrt2MB))`
`implies2^(5/4)=2pisqrt((2I)/(sqrt2MB))`
When one magnet is removed, `T_(2)=2pisqrt((I)/(MB))`
`implies 2^(5/4)/T_(2)=sqrt((2)/sqrt2)=2^(1/4)`
`T_(2)=2^(5/4)/2^(1/4)=2`