Two tangent galvanometers having coils of the same radius are connected in series. $A$ current flowing in them produces deflections of $60^{\circ}$ and $45^{\circ}$ respectively. The ratio of the number of turns in the coils is

$A$ magnet oscillating in a horizontal plane has a time period of $2 \ s$ at a place where the angle of dip is $30^o$ and $3 \ s$ at another place where the angle of dip is $60^o$. The ratio of resultant magnetic fields at the two places is

$A$ bar magnet has a magnetic moment equal to $5 \times 10^{-5} \, \text{Wb} \cdot \text{m}$. It is suspended in a magnetic field which has a magnetic induction $B$ equal to $8\pi \times 10^{-4} \, \text{T}$. The magnet vibrates with a period of vibration equal to $15 \, \text{s}$. The moment of inertia of the magnet is:

The time period of a bar magnet suspended horizontally in the earth's magnetic field and allowed to oscillate:

With a standard rectangular bar magnet, the time period of a vibration magnetometer is $4 \,s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of the vibration magnetometer when one piece is used (in seconds) (bar magnet breadth is small) is

The tangent galvanometer,when connected in series with a standard resistance,can be used as: