Magnets A and B are geometrically similar,but | vedclass

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(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

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

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(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:

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