At a certain place,a magnet makes $30$ oscillations per minute. At another place,if the magnetic induction is increased to two times the magnetic induction at the first place,then the time period of the same magnet will be:

To compare magnetic moments of two magnets by vibration magnetometer,the 'sum and difference method' is better because:

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.)

$A$ thin rectangular magnet suspended freely has a period of oscillation equal to $T$. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T'$,then the ratio $\frac{T'}{T}$ is

Two bar magnets $A$ and $B$ are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make $20$ oscillations per minute when the similar poles of $A$ and $B$ are on the same side,while they make $15$ oscillations per minute when their opposite poles lie on the same side. If $M_A$ and $M_B$ are the magnetic moments of $A$ and $B$ and if $M_A > M_B$,the ratio of $M_A$ and $M_B$ is

$A$ bar magnet is oscillating in the earth's magnetic field with a time period $T$. If a similar magnet with the same mass and volume has a magnetic dipole moment which is $9$ times that of this magnet,then its time period will be . . . . . . .