The periodic time of a magnet in a vibration magnetometer is $T_0$. If the magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then the time period of the new magnet will be:

Two short magnets having magnetic moments in the ratio $27 : 8$,when placed on opposite sides of a deflection magnetometer,produce no deflection. If the distance of the weaker magnet is $0.12 \ m$ from the centre of the deflection magnetometer,the distance of the stronger magnet from the centre is.......$m$

$A$ 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 $T$. If it is divided into four equal parts along its axis and perpendicular to its axis as shown,then the time period for each part will be

$A$ magnet is suspended in the magnetic meridian with an untwisted wire. The upper end of the wire is rotated through $180^o$ to deflect the magnet by $30^o$ from the magnetic meridian. When this magnet is replaced by another magnet,the upper end of the wire is rotated through $270^o$ to deflect the magnet $30^o$ from the magnetic meridian. The ratio of the magnetic moments of the magnets is

$A$ short magnet oscillates with a frequency $10 \, Hz$ where the horizontal component of Earth's magnetic field is $12 \, \mu T$. $A$ downward current of $15 \, A$ is established in a vertical wire placed $20 \, cm$ west of the magnet. The new frequency of the magnet is (in $ \, Hz$)