$A$ magnet freely suspended in a vibration magnetometer makes $40$ oscillations per minute at place $A$ and $20$ oscillations per minute at a place $B$. If the horizontal component of earth's magnetic field at $A$ is $36 \times 10^{-6} \ T$, then its value at $B$ is

$A$ short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at $14 \; cm$ from the centre of the magnet. The earth's magnetic field at the place is $0.36 \; G$ and the angle of dip is zero. What is the total magnetic field (in $G$) on the normal bisector of the magnet at the same distance as the null-point (i.e.,$14 \; cm$) from the centre of the magnet? (At null points,field due to a magnet is equal and opposite to the horizontal component of earth's magnetic field.)

$A$ bar magnet is oscillating in the earth's magnetic field with a time period $T$. If a similar magnet with the same mass and volume has a magnetic dipole moment which is $9$ times that of this magnet,then its time period will be . . . . . . .

$A$ short bar magnet with its north pole facing north forms a neutral point at $P$ in the horizontal plane. If the magnet is rotated by $90^o$ in the horizontal plane,the net magnetic induction at $P$ is (Horizontal component of earth's magnetic field = $B_H$)

$A$ dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2$ seconds. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2$ seconds. Then the angle of dip is.....$^o$

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 \ Hz$ when like poles are tied together and it is $2 \ Hz$ when the unlike poles are tied together, then the ratio $M_1: M_2$ is