A magnet of magnetic moment M oscillating freely in earth's horizontal magnetic field makes n oscillations per minute. If the magnetic moment is quadrupled and the earth's field is doubled, the number of oscillations made per minute would be

1. $\frac{n}{2\sqrt{2}}$                         2. $\frac{n}{\sqrt{2}}$

3. $2\sqrt{2}n$                        4. $\sqrt{2}n$

Magnets \(A\) and \(B\) are geometrically similar but the magnetic moment of \(A\) is twice that of \(B\). If \(T_1\) and \(T_2\) be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then \(\frac{T_1}{T_2}\) will be:
1. \(\frac{1}{3}\)
2. \(\frac{1}{2}\)
3. \(\frac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)

A magnetic needle suspended by a silk thread is vibrating in the earth's magnetic field. If the temperature of the needle is increased by 500°C, then

1. The time period decreases

2. The time period remains unchanged

3. The time period increases

4. The needle stops vibrating

The time period of oscillation of a bar magnet suspended horizontally along the magnetic meridian is T₀. If this magnet is replaced by another magnet of the same size and pole strength but with double the mass, the new time period will be

1. $\frac{T_0}{2}$                           

2. $\frac{T_0}{\sqrt{2}}$

3. $\sqrt{2}{T}_0$                        

4. 2T₀

The magnet of a vibration magnetometer is heated so as to reduce its magnetic moment by 19%. By doing this the periodic time of the magnetometer will

1. Increase by 19%       2. Decrease by 19%

3. Increase by 11%       4. Decrease by 21%

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 \(T'\), then ratio \(\frac{T'}{T}\) is:
1. \(\frac{1}{4}\)
2. \(\frac{1}{2\sqrt{2}}\)
3. \(\frac{1}{2}\)
4. \(2\)

Two identical short bar magnets, each having magnetic moment M, are placed a distance of 2d apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

1.  $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{2}\right) \frac{M}{d^3}$           2.  $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{3}\right) \frac{M}{d^3}$

3.  $\left(\frac{2{\mu }_0}{4\mathrm{\pi }}\right)\frac{M}{d^3}$                 4. $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{5}\right) \frac{M}{d^3}$

A superconductor exhibits perfect :

1. Ferrimagnetism              

2. Ferromagnetism

3. Paramagnetism              

4. Diamagnetism

Among the following properties describing diamagnetism identify  the property that is wrongly stated

1. Diamagnetic material do not have permanent magnetic moment

2. Diamagnetism is explained in terms of electromagnetic induction

3. Diamagnetic materials have a small positive susceptibility

4. The magnetic moment of individual electrons neutralize each other

If a magnet is suspended at an angle 30^o to the magnetic meridian, it makes an angle of 45^o with the horizontal. The real dip is

1. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

2. ${\tan }^{-1}\left(\sqrt{3}\right)$

3. ${\tan }^{-1}\left(\sqrt{\frac{3}{2}}\right)$

4. ${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$