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

The following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole. Which configuration has the highest net magnetic dipole moment? 

1.		2.
3.		4.

A bar magnet of length L and magnetic dipole moment M is bent in the form of an are as shown in figure. The new magnetic dipole moment will be


(1)M

(2)3M/π

(3)2/πM

(4)M/2

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3}$ J of work to turn it through $60°$. The torque needed to maintain the needle in this position will be

1. $2\sqrt{3}$J                     

2. 3 J

3. $\sqrt{3}$ J                       

4. $\frac{3}{2}$ J

There are four light-weight-rod samples; A, B, C, D separately suspended by threads. A bar magnet is slowly brought near each sample and the following observations are noted:

(i) A is feebly repelled 

(ii) B is feebly attracted

(iii) C is strongly attracted

(iv) D remains unaffected

Which one of the following is true?

1. C is of a diamagnetic material

2. D is of a ferromagnetic material

3. A is of a non-magnetic material

4. B is of a paramagnetic material

A short bar magnet of magnetic moment \(0.4\) JT^–1 is placed in a uniform magnetic field of \(0.16\) T. The magnet is in stable equilibrium when the potential energy is:
1. \(0.064\) J
2. zero
3. \(-0.082\) J
4. \(-0.064\) J

A vibration magnetometer placed in a magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2s in earth's horizontal magnetic field of 24 $\mu$T. When a horizontal field is 18 $\mu$T is produced opposite to the earth's field by placing a current-carrying wire, the new time period of the magnet will be

(a) 1s          (b) 2s

(c) 3s          (d) 4s

 Electromagnets are made of soft iron because soft iron has: