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. \(M, m\)

Two equal bar magnets are kept as shown in the figure. The direction of the resultant magnetic field, indicated by arrowhead at the point \(P\) is: (approximately)

1.		2.
3.		4.

If a magnetic needle is made to vibrate in uniform field \(H\), then its time period is \(T\). If it vibrates in the field of intensity \(4H\), its time period will be:

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 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. \(2\)

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. \(2^\frac{3}{4}\)

Two magnets \(A\) and \(B\) are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point \(P\) which gets deflected through an angle \(\theta\) under the influence of magnets. The ratio of distance \(d_1\) and \(d_2\) will be:
   
1. \((2\tan\theta)^{\frac{1}{3}}\)
2. \((2\tan\theta)^{\frac{-1}{3}}\)
3. \((2\cot\theta)^{\frac{1}{3}}\)
4. \((2\cot\theta)^{\frac{-1}{3}}\)

A current-carrying loop is placed in a uniform magnetic field in four different orientations, I, II, III & IV. The decreasing order of potential energy is:

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. \(\frac{2 W}{\sqrt{3}}\)