When $\sqrt{3} \text{ A}$ current is passed in a tangent galvanometer,there is a deflection of $30^{\circ}$. The deflection obtained when $3 \text{ A}$ current is passed is.....$^{\circ}$

The magnetic needle of a vibration magnetometer makes $12$ oscillations per minute in the horizontal component of earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line, it makes $15$ oscillations per minute. If the poles of the bar magnet are interchanged, the number of oscillations it makes per minute is

The time period of a vibration magnetometer is $T_0$. Its magnet is replaced by another magnet whose moment of inertia is $3$ times and magnetic moment is $1/3$ of the initial magnet. The time period now will be

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $2 \, s$. The magnet is cut along its length into three equal parts and these three parts are then placed on each other with their like poles together. The time period of this combination will be

Two bar magnets of the same mass,length,and breadth,but with magnetic moments $M$ and $2M$ respectively,have a time period of $3 \, s$ when placed in the same position (sum position). What will be the time period when they are placed in the different position (difference position)?

$A$ vibration magnetometer is used at two different places $A$ and $B$ on the earth. The time period of a magnet suspended freely in the magnetometer at $A$ is twice that at $B$. If the horizontal component of the earth's magnetic field at $B$ is $32 \times 10^{-6} \,T$, then its value at $A$ is