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^(3//4)`

Answer

c

Explanation

(c) Initially magnetic moment of system
`M_(1)=sqrt(M^(2)+M^(2))=sqrt2M` 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))xx(M_(2))/(M_(1)))=sqrt((2I)/(I)xx(M)/(sqrt2M))`
`rArrT_(2)=(2^(5//4))/(2^(1//4))=2sec`