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.......$m$

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

The time period of oscillation of a magnet is $2 \ s$. When it is remagnetised so that its pole strength is $4$ times,its period will be ..... $s$.

The period of oscillation of a bar magnet at a place is $2 \,s$. At the same place, the period of oscillation of another identical bar magnet whose magnetic moment is $4$ times that of the first magnet is: (in $\,s$)

Magnetic moments of two bar magnets may be compared with the help of

$A$ deflection magnetometer is adjusted and a magnet of magnetic moment $M$ is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needle before settling of the deflection is $T$. When the magnet is removed, the period of oscillation of the needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's horizontal magnetic field is $B_H$, the relation between $T$ and $T_0$ is