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

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $T$. The magnet is cut along its length into six parts and these parts are then placed together as shown in the figure. The time period of this combination will be

In a uniform magnetic field,a magnetic needle has a magnetic moment $9.85 \times 10^{-2} \, A \cdot m^{2}$ and a moment of inertia $5 \times 10^{-6} \, kg \cdot m^{2}$. If it performs $10$ complete oscillations in $5 \, s$,then the magnitude of the magnetic field is $.... \, mT$. [ Take $\pi^{2} = 9.85$ ]

The periodic time of a magnet in a vibration magnetometer is $T_0$. If the magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then the time period of the new magnet will be:

The strength of the magnetic field in which the magnet of a vibration magnetometer is oscillating is increased $4$ times its original value. The frequency of oscillation would then become

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