$A$ bar magnet is oscillating in the earth's magnetic field with time period $T.$ If its mass is increased four times,then its time period will be

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 \ Hz$ when like poles are tied together and it is $2 \ Hz$ when the unlike poles are tied together, then the ratio $M_1: M_2$ is

$A$ 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.)

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $T$. The magnet is cut along its length into six parts and these parts are then placed together as shown in the figure. The time period of this combination will be

At a certain place, a magnet makes $30$ oscillations per minute. At another place where the magnetic field is double, its time period will be:

In a uniform magnetic field of $0.049 \ T$, a magnetic needle performs $20$ complete oscillations in $5 \ s$. The moment of inertia of the needle is $9.8 \times 10^{-5} \ kg \ m^2$. If the magnitude of the magnetic moment of the needle is $x \times 10^{-5} \ A \ m^2$, then the value of '$x$' is: (in $\pi^2$)