The magnetic needle of a tangent galvanometer is deflected at an angle $30^\circ$ due to a magnet. The horizontal component of Earth's magnetic field $0.34 \times 10^{-4} \, T$ is along the plane of the coil. The magnetic intensity is

The time period of a vibration magnetometer is $T_0$. Its magnet is replaced by another magnet whose moment of inertia is $3$ times and magnetic moment is $1/3$ of the initial magnet. The time period now will be

$A$ vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is $2^{5/4} \ s$. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is:

The time period of a magnet is $2 \, s$. The horizontal component of the Earth's magnetic field is $H$. When an external magnetic field $F$ is applied in the same direction,the new time period becomes $1 \, s$. What is the ratio $H/F$?

$A$ short bar magnet having a 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 time period of oscillation of a magnet in a vibration magnetometer is $1.5 \ s$. The time period of oscillation of another magnet similar in size,shape,and mass but having one-fourth magnetic moment than that of the first magnet,oscillating at the same place,will be.....$s$.