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The magnet of pole strength m and magnetic moment M, is cut into two pieces, along its axis. Its pole strength and magnetic moment now become
1. $\frac{\mathrm{m}}{2},\frac{M}{2}$
2. $m,\frac{M}{2}$
3. $\frac{\mathrm{m}}{2},\mathrm{M}$
4. m,M

If the areas under the I-H hysteresis loop and B-H hysteresis loop are denoted by ${\mathrm{A}}_1 \mathrm{and} {\mathrm{A}}_2$, then 
1. ${\mathrm{A}}_2={\mathrm{\mu }}_0{\mathrm{A}}_1$
2. ${\mathrm{A}}_2={\mathrm{A}}_1$
3. ${\mathrm{A}}_2=\frac{{\mathrm{A}}_1}{{\mathrm{\mu }}_0}$
4. ${\mathrm{A}}_2={\mathrm{\mu }}_0^2{\mathrm{A}}_1$

Two magnets A and B are identical and these are arranged as shown in the figure. Their lengths are negligible in comparision to the separation between them. A magnetic needle is placed between the magnets at point P and it gets delfected by an angle $\mathrm{\theta }$. The ratio of distances ${\mathrm{d}}_1 \mathrm{and} {\mathrm{d}}_2$, will be

1. ${\left(2 \mathrm{cot\theta }\right)}^{1/3}$
2. ${\left(2 \tan \mathrm{\theta }\right)}^{1/3}$
3. ${\left(2 \mathrm{cot\theta }\right)}^{-1/3}$
4. ${\left(2 \tan \mathrm{\theta }\right)}^{-1/3}$

A bar magnet has pole strength 3.6 A-m and length 12 cm. Its area of cross section is 0.9 cm². The magnetic field at the centre of the bar magnet is 
1. $6\times {10}^{-3} \mathrm{T}$
2. $5\times {10}^{-2} \mathrm{T}$
3. $2.5\times {10}^{-2} \mathrm{T}$
4. $2.5\times {10}^{-8} \mathrm{T}$

The magnetic susceptibility of a paramagnetic substance at -73$°$C is 0.0060, then its value at -173$°$C will be 
1. 0.0030
2. 0.0120
3. 0.0180
4. 0.0045

A deflection magnetometer is adjusted in the usual way. When a magnet is introduced, the deflection observed is $\mathrm{\theta }$, and the period of oscillation of the neddle in the magnetometer is T. When the magnet is removed, the period of oscillation is T₀. The relation between T and T₀ is 
1. ${\mathrm{T}}^2={\mathrm{T}}_0^2\cos \mathrm{\theta }$
2. ${\mathrm{T}}^2={\mathrm{T}}_0\cos \mathrm{\theta }$
3. $\mathrm{T}=\frac{{\mathrm{T}}_0}{\cos \mathrm{\theta }}$
4. $\mathrm{T}=\frac{{\mathrm{T}}_0^2}{\cos \mathrm{\theta }}$

Two magnets are suspended by a given wire, one by one. In order to deflect the first magnet through 45$°$, the wire has to be twisted through 540$°$ whereas for the second magnet, the wire requires a twist of 360$°$ for producing the same direction. Then, the ratio of magnetic moments of the two is 
1. 11/7
2. 3/2
3. 4/3
4. 7/6

The plane of dip circle is set in the geographic meridian and the apparant dip is ${\mathrm{\delta }}_1$. It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is ${\mathrm{\delta }}_2$. The declination $\mathrm{\theta }$ at the place is 
1. $\mathrm{\theta }={\tan }^{-1}\left({\mathrm{tan\delta }}_1{\mathrm{tan\delta }}_2\right)$
2. $\mathrm{\theta }={\tan }^{-1}\left({\mathrm{tan\delta }}_1+{\mathrm{tan\delta }}_2\right)$
3. $\mathrm{\theta }={\tan }^{-1}\left(\frac{{\mathrm{tan\delta }}_1}{{\mathrm{tan\delta }}_2}\right)$
4. $\mathrm{\theta }={\tan }^{-1}\left({\mathrm{tan\delta }}_1-{\mathrm{tan\delta }}_2\right)$

A bar magnet suspended by a suspension fibre, is placed in the magnetic meridian with no twist in the suspension fibre. On turning the upper end of the suspension fibre by an angle of 120$°$ from the meridian, the magnet is deflected by an angle of 30$°$ from the meridian. Then, the angle by which the upper end of the suspension fibre has to be twisted. so as to deflect the magnet through 90$°$ from the meridian is 
1. 270$°$
2. 240$°$
3. 330$°$
4. 180$°$

A magnetic dipole of magnetic moment M is rotated through 360$°$ in a magnetic field B. The work done will be 
1. MB
2. 2MB
3. $2\mathrm{\pi MB}$
4. zero

A short magnet oscillated with a time period 0.1 s at a place where horizontal magnetic field is 24 $\mathrm{\mu T}$. A downward current of 18 A is established in a vertical wire 20 cm east of the magnet. The new time period of oscillator 
1. 0.1 s
2. 0.089 s
3. 0.076 s
4. 0.057 s

A short bar magnet placed with its axis at 30$°$ with a uniform external magnetic field of 0.16 T, experiences a torque of magnitude 0.032 J. The magnetic moment of the bar magnet will be 
1. 0.23 ${\mathrm{JT}}^{-1}$
2. 0.40 ${\mathrm{JT}}^{-1}$
3. 0.80 ${\mathrm{JT}}^{-1}$
4. zero

M and $\mathrm{M}\sqrt{3}$ are the magnetic dipole moments of the two magnets, which are joined to from a cross figure. The inclination of the system with the field, if their combination is suspended freely in a uniform external magnetic field B is 

1. $\mathrm{\theta }=30°$
2. $\mathrm{\theta }=45°$
3. $\mathrm{\theta }=60°$
4. $\mathrm{\theta }=15°$

The value of $\frac{{\mathrm{\delta B}}_{\mathrm{x}}}{\mathrm{\delta x}}+\frac{{\mathrm{\delta B}}_y}{\mathrm{\delta y}}+ \frac{{\mathrm{\delta B}}_z}{\mathrm{\delta z}}$ is 
1. >0
2. <0
3. $\ge 0$
4. =0

Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 2M, respectively are joined together pole to pole and suspended by a string. The time period of the assembly in a magnetic field of strength H is 3 seconds. If now the polarity of one of the magnetis is reversed and the combination is again made to oscillate in the same field, the time of oscillation is 
1. 3 s
2. $3\sqrt{3}$s
3. $3/\sqrt{3}$ s
4. 6 s