$A$ short magnet of magnetic moment $6.75 \, Am^2$ produces a neutral point on its axis. If the horizontal component of the Earth's magnetic field is $5 \times 10^{-5} \, Wb/m^2$, then the distance of the neutral point from the center of the magnet is.....$cm$.

Two different magnets are tied together and allowed to vibrate in a horizontal plane. When their like poles are joined,the time period of oscillation is $5 \, s$,and when their unlike poles are joined,the time period of oscillation is $15 \, s$. The ratio of their magnetic moments is

Two tangent galvanometers,which are identical except in their number of turns,are connected in parallel. The ratio of their resistances of the coils is $1 : 3$. If the deflections in the two tangent galvanometers are $30^{\circ}$ and $60^{\circ}$ respectively,then the ratio of their number of turns 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.)

$A$ current of $\left(\frac{2}{\sqrt{3}}\right) \text{ A}$ produces a deflection of $60^{\circ}$ in a tangent galvanometer. The reduction factor is:

$A$ compass needle of an oscillation magnetometer oscillates $20$ times per minute at a place $P$ where the angle of dip is $30^{\circ}$. The number of oscillations per minute becomes $10$ at another place $Q$ where the angle of dip is $60^{\circ}$. The ratio of the total magnetic field at the two places $(B_{Q}: B_{P})$ is: