Vibration Magnetometer

The periodic time of a magnet in vibration magnetometer is $T_0$. If a magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then time period of new magnet will be

The frequency of oscillation of a small magnet in a magnetic field of induction 'B' is '$n$'. If the frequency of oscillations of the same magnet in a field of induction 'X' falls to $\left(\frac{n}{3}\right)$, the value of 'X' is

Two bar magnets A and B are geometrically similar but the magnetic moment of $A$ is twice that of $B.\ T_1$ is the time period of oscillation when their like poles are kept together. When unlike poles are kept together, the time period of oscillation is $T_2$. The ratio $T_1 : T_2$ will be

A magnetic needle of magnetic moment $6 \times 10^{-2}\text{ Am}^{2}$ and moment of inertia $9.6 \times 10^{-5}\text{ kg m}^{2}$ performs simple harmonic motion in a magnetic field of 0.01 T. Time taken to complete 10 oscillations is [Take $\pi = 3.14$]

The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0 \times 10^{-2}\text{ A m}^{2}$ and $\frac{10^{-6}}{\pi^{2}}\text{ kg m}^{2}$. If it completes 10 oscillations in $10\text{ s}$, the magnitude of the magnetic field is

In a uniform magnetic field of $0.049\text{ T}$, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6}\text{ kg m}^{2}$. If the magnitude of magnetic moment of the needle is $x \times 10^{-5}\text{ Am}^{2}$, then the value of '$x$' is:

At certain place a magnet makes 30 oscillations per minute. At another place if the magnetic induction is increased by two times the magnetic induction at first place, then the time period of same magnet will be

A compass needle oscillates 20 times per minute at a place where the dip is $30^\circ$ and 30 times per minute where the dip is $60^\circ$. The ratio of total magnetic field due to the earth at two places respectively is $\frac{4}{\sqrt{x}}$. The value of $x$ is

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $3\text{ s}$ and $4\text{ s}$ respectively. If their moments of inertia are in the ratio of $3 : 2$, then the ratio of their magnetic moments will be:

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place $\mathrm{P}$ of $\text{dip } 30^\circ$. The number of oscillations per minute become 10 at another place $\mathrm{Q}$ of $60^\circ$ dip. The ratio of the total magnetic field at the two places $(B_Q : B_P)$ is:

Two bar magnets '$\mathrm{P}$' and '$\mathrm{Q}$' are kept in uniform magnetic field '$\mathrm{B}$' with magnetic moments '$\mathrm{M}_{\mathrm{P}}$' and '$\mathrm{M}_{\mathrm{Q}}$' respectively. Magnet 'P' is oscillating with frequency twice that of magnet 'Q'. If the moment of inertia of the magnet 'P' is twice that of magnet 'Q' then

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 $\times$ 10$-$2 A m2 and moment of inertia 5 $\times$ 10$-$6 kg m2. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _______________ mT. [Take $\pi$2 as 9.85]

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio $\frac{B_1}{B_2}$ is best given by:

A magnetic needle of magnetic moment 6.7 $\times$ 10−2 A m2 and moment of inertia 7.5 $\times$ 10−6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

A vibration magnetometer placed in magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2 sec in earth's horizontal magnetic field of 24 microtesla. When a horizontal field of 18 microtesla is produced opposite to the earth's field by placing a current carrying wire, the new time period of magnet 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 $2\text{ s.}$ The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

A bar magnet is oscillating in the Earth's magnetic field with a period T. What happens to its period and motion if its mass is quadrupled?

A thin rectangular magnet suspended freely has a period of oscillation equal to $T.$ Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T',$ the ratio $\frac{T'}{T}$ is

Two bar magnets having same geometry with magnetic moments M and 2M, are firstly placed in such a way that their similar poles are same side then its time period of oscillation is T1. Now the polarity of one of the magnet is reversed then time period of oscillation is T2, then

A bar magnet is oscillating in the Earth's magnetic field with a period $T$. What happens to its period and motion if its mass is quadrupled?