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. $\frac{2m}{eJ}$

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

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 bar magnet has coercivity $4\times {10}^3 A{m}^{-1}$. It is desired to demagnetize it by inserting it inside a solenoid 12 cm long and having 60 turns. The current that should be sent through the solenoid is

1. 2 A                            2. 4 A

3. 6 A                            4. 8 A

If ${\theta }_1 and {\theta }_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by 

1. $co{t}^2\theta =co{t}^2{\theta }_1+co{t}^2{\theta }_2$

2. ${\tan }^2\theta ={\tan }^2{\theta }_1+ {\tan }^2{\theta }_2$

3. $co{t}^2\theta =co{t}^2{\theta }_1-{\tan }^2{\theta }_2$

4. ${\tan }^2\theta ={\tan }^2{\theta }_1-{\tan }^2{\theta }_2$

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by \(60^{\circ}\) is \(W\). Now the torque required to keep the magnet in this new position is:
1. \(\frac{W}{\sqrt{3}}\) 
2. \(\sqrt{3} W\)
3. \(\frac{\sqrt{3} W}{2}\) 
4. \(\frac{2 W}{\sqrt{3}}\)

The magnetic susceptibility is negative for

1. paramagnetic material only

2. ferromagnetic material only

3. paramagnetic and ferromagnetic materials

4. diamagnetic material only