When two magnets of equal pole strength and length are placed with their dissimilar poles on the same side,what will be their time period?

Two short magnets having magnetic moments in the ratio $27 : 8$,when placed on opposite sides of a deflection magnetometer,produce no deflection. If the distance of the weaker magnet is $0.12 \ m$ from the centre of the deflection magnetometer,the distance of the stronger magnet from the centre is.......$m$

$A$ magnet is suspended horizontally in the earth's magnetic field. When it is displaced and then released,it oscillates in a horizontal plane with a period $T$. If a piece of wood of the same moment of inertia (about the axis of rotation) as the magnet is attached to the magnet,what would the new period of oscillation of the system become?

Two magnets are placed with their like poles together,and they perform $12$ oscillations in $1$ minute. When they are placed with their unlike poles together,they perform $4$ oscillations in $1$ minute. What is the ratio of the magnetic moments of the magnets?

Two mutually perpendicular uniform magnetic fields $F$ and $H$ act on a magnetic needle. The needle makes an angle of $60^\circ$ with the field $F$. Find the ratio $\frac{F}{H}$.

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