$A$ 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$)

Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the Earth's magnetic field. With like poles of magnets together,$12$ oscillations per minute are made,but for unlike poles together,only $4$ oscillations per minute are executed. The ratio of their magnetic moments is

At a certain place,a magnet makes $30$ oscillations per minute. At another place where the magnetic field is doubled,its time period will be

$A$ tangent galvanometer has $80$ turns of wire. The internal and external diameters of the coil are $19 \, cm$ and $21 \, cm$ respectively. The reduction factor of the galvanometer at a place where $H = 0.32 \, \text{oersted}$ will be $(1 \, \text{oersted} = 80 \, A/m)$.

$A$ short magnetic needle is pivoted in a uniform magnetic field of strength $1 \, T$. When another magnetic field of strength $\sqrt{3} \, T$ is applied to the needle in a perpendicular direction,the needle deflects through an angle $\theta$. The value of $\theta$ is: (in $^o$)

The magnet of a vibration magnetometer is heated so as to reduce its magnetic moment by $19\%$. By doing this,the periodic time of the magnetometer will