The frequency of oscillation of a small magnet in a magnetic field of induction $B$ is $n$. If the frequency of oscillations of the same magnet in a field of induction $X$ falls to $n/3$, the value of $X$ is

Two mutually perpendicular uniform magnetic fields $F$ and $H$ act on a magnetic needle. The needle makes an angle of $60^\circ$ with the field $F$. Find the ratio $\frac{F}{H}$.

$A$ 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:

$A$ bar magnet of $10 \,cm$ length is kept with its north $(N)$-pole pointing north. $A$ neutral point is formed at a distance of $15 \,cm$ from each pole. Given the horizontal component of Earth's magnetic field is $0.4 \,Gauss$, the pole strength of the magnet is: (in $\,A-m$)

$A$ 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 time period in a vibration magnetometer will be infinity at