Magnets A and B are geometrically similar,but | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The time period of oscillation for a vibration magnetometer is given by $T = 2\pi \sqrt{\frac{I}{MB_H}}$,where $I$ is the moment of inertia,$M$ is

Vedclass · Accepted Answer

$\frac{1}{\sqrt{3}}$

Vedclass · Answer

(C) The time period of oscillation for a vibration magnetometer is given by $T = 2\pi \sqrt{\frac{I}{MB_H}}$,where $I$ is the moment of inertia,$M$ is the magnetic moment,and $B_H$ is the horizontal component of the Earth's magnetic field.For two magnets $A$ and $B$ with moments $M_1 = 2M$ and $M_2 = M$,and moments of inertia $I_1$ and $I_2$,when placed together:When like poles are together,the effective magnetic moment is $M_{sum} = M_1 + M_2 = 3M$. The time period is $T_1 = 2\pi \sqrt{\frac{I_1 + I_2}{(M_1 + M_2)B_H}}$.When unlike poles are together,the effective magnetic moment is $M_{diff} = M_1 - M_2 = 2M - M = M$. The time period is $T_2 = 2\pi \sqrt{\frac{I_1 + I_2}{(M_1 - M_2)B_H}}$.Taking the ratio: $\frac{T_1}{T_2} = \sqrt{\frac{M_1 - M_2}{M_1 + M_2}} = \sqrt{\frac{2M - M}{2M + M}} = \sqrt{\frac{M}{3M}} = \frac{1}{\sqrt{3}}$.

Magnets $A$ and $B$ are geometrically similar,but the magnetic moment of $A$ is twice that of $B$. If $T_1$ and $T_2$ are the time periods of oscillation when their like poles and unlike poles are kept together respectively,then the ratio $\frac{T_1}{T_2}$ will be:

Similar Questions

$A$ vibration magnetometer is placed at the south pole; then its time period will be

$A$ magnet oscillating in a horizontal plane has a time period of $2 \ s$ at a place where the angle of dip is $30^o$ and $3 \ s$ at another place where the angle of dip is $60^o$. The ratio of resultant magnetic fields at the two places is

The radius of the coil of a Tangent galvanometer,which has $10$ turns,is $0.1\,m$. The current required to produce a deflection of $60^{\circ}$ $(B_H = 4 \times 10^{-5}\,T)$ is.....$A$

$A$ compass needle oscillates $20$ times per minute at a place where the dip is $45^{\circ}$ and the magnetic field is $B_1$. The same needle oscillates $30$ times per minute at a place where the dip is $30^{\circ}$ and magnetic field is $B_2$. Then $B_1: B_2$ is

At two places $A$ and $B$,using a vibration magnetometer,a magnet vibrates in a horizontal plane. Its respective periodic times are $2 \ s$ and $3 \ s$. At these places,the Earth's horizontal components are $H_A$ and $H_B$ respectively. Then the ratio between $H_A$ and $H_B$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module