The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is:
1. $2^{-3}$

2. $2^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

3. $2^3$

4. $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

A magnet of magnetic moment 20 C.G.S. units are freely suspended in a uniform magnetic field of intensity 0.3 C.G.S. units. The amount of work done in deflecting it by an angle of ${30}^o$ in C.G.S. units is
(1) 6

(2) $3\sqrt{3}$

(3) $3(2-\sqrt{3})$

(4) 3

The magnetic field due to a short magnet at a point on its axis at a distance X cm from the middle point of the magnet is 200 Gauss. The magnetic field at a point on the neutral axis at a distance of X cm from the middle of the magnet is:

1. 100 Gauss

2. 400 Gauss

3. 50 Gauss

4. 200 Gauss

A sensitive magnetic instrument can be shielded very effectively from outside magnetic fields by placing it inside a box of
1. Teak wood
2. Plastic material
3. Soft iron of high permeability
4. A metal of high conductivity

A uniform magnetic field, parallel to the plane of the paper existed in space initially directed from left to right. When a bar of soft iron is placed in the field parallel to it, the lines of force passing through it will be represented by

1. 

2.  

3. 

4. 

$1. \tau =niAB\cos \theta$
$2. \tau =niAB\sin \theta$
$3. \tau =niAB$
$4. None of the above$

If a bar magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B, the work done in rotating the magnet through an angle is

1. $MB(1-\sin \theta )$

2. $MB\sin \theta$

3. $MB\cos \theta$

4. $MB(1-\cos \theta )$

A magnet of magnetic moment M is situated with its axis along the direction of a magnetic field of strength B. The work done in rotating it by an angle of 180^o will be

(1) -MB                        

(2) +MB

(3) 0                            

(4) +2MB

A magnetic needle is kept in a non-uniform magnetic field. It experiences:

1. A force and a torque

2. A force but not a torque

3. A torque but not a force 

4. Neither a torque nor a force

A long magnetic needle of length 2L, magnetic moment M and pole strength m units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be:

1. $\frac{M}{2},\frac{m}{2}$

2. $M,\frac{m}{2}$

3. $\frac{M}{2},m$

4. M, m