A vibraiton magnetometer consits of two idential bar magnets placed one over the other such that they are mutually perpendicular and bisect each other. The time period of oscillations of combination in a horizontal magnetic field is `4s`. If one of the magnets is removed, then the period of oscillations of the other in teh same field is

Options

A. `5 .78 s `
B. `3 .36 s`
C. `4 .36 s `
D. `5 .36 s`

Answer

B

Explanation

As magnets are perpendicular to each other, the resultant magnetic moment
`M . = sqrt ( M ^(2) + M ^(2)) = sqrt2 M`
`therefore T _(1) = 2pi sqrt (( 2 I )/(( sqrt2 M ) B))`
In the second case, `T _(2) = 2pi sqrt (( I )/( MB))`
`(T _(2))/( T _(1)) = ( 1)/((2) ^( 1//4))`
`therefore T _(2) = (4)/(( 2) ^(1//4) ) = 3 .36 s`