The period of oscillation of a vibration magnetometer depends on which of the following factors? (where $I$ is the moment of inertia of the magnet about the axis of suspension,$M$ is the magnetic moment of the magnet,and $H$ is the external magnetic field.)

$A$ short bar magnet having magnetic moment $4 \text{ Am}^2$, placed in a vibrating magnetometer, vibrates with a time period of $8 \text{ s}$. Another short bar magnet having a magnetic moment $8 \text{ Am}^2$ vibrates with a time period of $6 \text{ s}$. If the moment of inertia of the second magnet is $9 \times 10^{-2} \text{ kg m}^2$, the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field.)

In the sum and difference method of a vibration magnetometer,the time period is greater if:

$A$ bar magnet of $10 \,cm$ length is kept with its north $(N)$-pole pointing north. $A$ neutral point is formed at a distance of $15 \,cm$ from each pole. Given the horizontal component of Earth's magnetic field is $0.4 \,Gauss$, the pole strength of the magnet is: (in $\,A-m$)

The period of oscillation of a magnet of a vibration magnetometer is $2.45 \,s$ at one place and $4.9 \,s$ at the other. The ratio of the horizontal component of earth's magnetic field at the two places is .........

The magnetic needle of a vibration magnetometer makes $12$ oscillations per minute in the horizontal component of earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line, it makes $15$ oscillations per minute. If the poles of the bar magnet are interchanged, the number of oscillations it makes per minute is