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

If the angular momentum of an electron is $\overrightarrow{J}$ then the magnitude of the magnetic moment will be

1. $\frac{eJ}{m}$                           
2. $\frac{eJ}{2m}$
3. ej.2m                         
4. $\frac{2m}{eJ}$

The basic magnetization curve for a ferromagnetic material is shown in the figure. Then, the value of relative permeability is highest for the point :

1. P         

2. Q

3. R         

4. S

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

The true value of angle of dip at a place is 60^o, the apparent dip in a plane inclined at an angle of 30^o with magnetic meridian is

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

2. ${\tan }^{-1}\left(2\right)$

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

4. None of these

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 \(2^{\frac{5}{4}}\) seconds. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is:
1. \(2^\frac{1}{4}\)
2. \(2^\frac{1}{2}\)
3. \(2\)
4. \(2^\frac{3}{4}\)

A cylindrical rod magnet has a length of 5 cm and a diameter of 1 cm. It has a uniform magnetization of 5.30 × 10³Amp/m³. What is its magnetic dipole moment?

1. $1\times {10}^{-2} J/T$                   

2. $2.08\times {10}^{-2} J/T$

3. $3.08\times {10}^{-2} J/T$              

4. $1.52\times {10}^{-2} J/T$