A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a place where dip angle is 30^o and 15 oscillations per minute at a place where dip angle is 60^o. The ratio of total earth's magnetic field at the two places is:

1. $3\sqrt{3}:8$
2. $16:9\sqrt{3}$
3. 4:9
4. $2\sqrt{3}:9$

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. \((2\cot\theta)^{\frac{-1}{3}}\)

For substances hysteresis (B - H) curves are given as shown in figure. For making temporary magnet which of the following is best?

1.		2.
3.		4.

The relative permeability $\left({\mu }_r\right)$ of a ferromagnetic substance varies with temperature (T) according to the curve:

1. A                              

2. B

3. C                              

4. D

The figure illustrates how B, the flux density, inside a sample of unmagnetized ferromagnetic material varies with B₀, the magnetic flux density, in which the sample is kept. For the sample to be suitable for making a permanent magnet:

1. OQ should be large and OR should be small

2. OQ and OR should both be large

3. OQ should be small and OR should be large

4. OQ and OR should both be small

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. \(\frac{2 W}{\sqrt{3}}\)