(B) The frequency of oscillation in a vibration magnetometer is given by $f = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.When magnets are placed together, th

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(B) The frequency of oscillation in a vibration magnetometer is given by $f = \frac{1}{2\pi} \sqrt{\frac{MB}{I}}$.When magnets are placed together, the effective magnetic moment is $M_{eff} = M_A + M_B$ (for similar poles) and $M_{eff} = M_A - M_B$ (for opposite poles).Let $f_s = 20 \text{ oscillations/min}$ and $f_d = 15 \text{ oscillations/min}$.Since $f \propto \sqrt{M_{eff}}$, we have $\frac{f_s}{f_d} = \sqrt{\frac{M_A + M_B}{M_A - M_B}}$.Squaring both sides: $\left(\frac{20}{15}\right)^2 = \frac{M_A + M_B}{M_A - M_B} \Rightarrow \left(\frac{4}{3}\right)^2 = \frac{M_A + M_B}{M_A - M_B} \Rightarrow \frac{16}{9} = \frac{M_A + M_B}{M_A - M_B}$.Using componendo and dividendo: $\frac{M_A}{M_B} = \frac{16+9}{16-9} = \frac{25}{7}$.

Class 12 Physics Magnetism and Matter Magnetic Equipment's (Tangent galvanometer, Vibration magnetometer and Neutral point)

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Two bar magnets $A$ and $B$ are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make $20$ oscillations per minute when the similar poles of $A$ and $B$ are on the same side, while they make $15$ oscillations per minute when their opposite poles lie on the same side. If $M_A$ and $M_B$ are the magnetic moments of $A$ and $B$ and if $M_A > M_B$, the ratio of $M_A$ and $M_B$ is

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A
$4:3$
B
$25:7$
C
$7:5$
D
$25:16$

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Class 12 Questions

Class 12

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Magnetism and Matter

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Magnetic Equipment's (Tangent galvanometer, Vibration magnetometer and Neutral point)

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$A$ dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2$ seconds. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2$ seconds. Then the angle of dip is.....$^o$

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$A$ magnetic needle oscillates in a horizontal plane with a period $T$ at a place where the angle of dip is $60^{\circ}$. When the same needle is made to oscillate in a vertical plane coinciding with the magnetic meridian,its period will be

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$A$ bar magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

DifficultAP EAMCET 2007

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$A$ deflection magnetometer is adjusted and a magnet of magnetic moment $M$ is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needle before settling of the deflection is $T$. When the magnet is removed, the period of oscillation of the needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's horizontal magnetic field is $B_H$, the relation between $T$ and $T_0$ is

DifficultAP EAMCET 2013

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The ratio of magnetic moments of two bar magnets is $13 : 5$. These magnets are held together in a vibration magnetometer and are allowed to oscillate in the Earth's magnetic field. When like poles are together,$15$ oscillations per minute are made. What will be the frequency of oscillation of the system if unlike poles are together? (in $oscillations/min$)

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$A$ dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2$ seconds. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2$ seconds. Then the angle of dip is.....$^o$

$A$ magnetic needle oscillates in a horizontal plane with a period $T$ at a place where the angle of dip is $60^{\circ}$. When the same needle is made to oscillate in a vertical plane coinciding with the magnetic meridian,its period will be

$A$ bar magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

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