A vibration magnetometer consist of two identical 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 the same field is

Explanation

For a vibration magnetometer, we known that
`T = 2pi sqrt((I)/(MB))`
Let M bet the magnetic moment and I be the moment of inertia of each magnet then ,
`M^(1) = sqrt(M^(2) + M^(2)) = sqrt(2)M and I^(1) = I + I =2I`
`:. T^(1) = 2pi sqrt((2I)/(sqrt(2)MB)) = 2pi xx sqrt((sqrt(2)I)/(MB))`.......... (1)
when one of the magnet is taken away then ,
`M^(1) = M, I^(11) = I`
` :. T^(11) = 2pi sqrt((I)/(MB))`............ (2)
`(eq(2))/(eq(1)) implies (T^(11))/(T^(1)) = (1)/((2)^(1//4)) of `
`T^(11) = (4)/((2)^(1//4)) = 3.36 ` sec.