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

$A$ magnet oscillating in a horizontal plane has a time period of $2 \ s$ at a place where the angle of dip is $30^o$ and $3 \ s$ at another place where the angle of dip is $60^o$. The ratio of resultant magnetic fields at the two places is

$A$ magnet makes $20$ and $15$ oscillations in $1$ minute at two places where the angles of dip are $30^{\circ}$ and $60^{\circ}$ respectively. What is the ratio of the total magnetic fields at these two places?

In a uniform magnetic field of $0.049 \ T$, a magnetic needle performs $20$ complete oscillations in $5 \ s$. The moment of inertia of the needle is $9.8 \times 10^{-5} \ kg \ m^2$. If the magnitude of the magnetic moment of the needle is $x \times 10^{-5} \ A \ m^2$, then the value of '$x$' is: (in $\pi^2$)

$A$ vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is $2^{5/4} \ s$. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is:

The moment of inertia of a magnetic needle is $40 \, g \cdot cm^2$ and it has a time period of $3 \, s$ in the Earth's horizontal magnetic field of $3.6 \times 10^{-5} \, Wb/m^2$. Its magnetic moment will be (in $A \cdot m^2$):