The length $l$ 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 into three equal parts of length $l/3$ each. If these parts are placed on each other with their like poles together,then the time period of this combination is

$A$ short bar magnet having magnetic moment $4 \text{ Am}^2$, placed in a vibrating magnetometer, vibrates with a time period of $8 \text{ s}$. Another short bar magnet having a magnetic moment $8 \text{ Am}^2$ vibrates with a time period of $6 \text{ s}$. If the moment of inertia of the second magnet is $9 \times 10^{-2} \text{ kg m}^2$, the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field.)

With a standard rectangular bar magnet of length $l$, breadth $b$ $(b \ll l)$ and magnetic moment $M$, the time period of the magnet in a vibration magnetometer is $4 \ s$. If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is

$A$ long vertical wire in which a current is flowing produces a neutral point with the Earth's magnetic field at a distance of $5 \ cm$ from the wire. If the horizontal component of the Earth's magnetic induction is $0.18 \ G$,then the current in the wire is: (in $A$)

$A$ bar-magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

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.....$^{\circ}$