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

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(C) The time period of a vibration magnetometer is given by $T = 2 \pi \sqrt{\frac{I}{MB}}$, where $I$ is the moment of inertia and $M$ is the magnetic moment.When the bar magnet is cut parallel to its length into four equal pieces, the mass of each piece becomes $m' = \frac{m}{4}$.The new moment of inertia of one piece about the axis of rotation is $I' = \frac{I}{4}$.The new magnetic moment of one piece is $M' = \frac{M}{4}$.Substituting these into the formula for the new time period $T'$:$T' = 2 \pi \sqrt{\frac{I'}{M' B}} = 2 \pi \sqrt{\frac{I/4}{(M/4) B}} = 2 \pi \sqrt{\frac{I}{MB}} = T$.Therefore, the new time period $T' = 4 \,s$.

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

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With a standard rectangular bar magnet, the time period of a vibration magnetometer is $4 \,s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of the vibration magnetometer when one piece is used (in seconds) (bar magnet breadth is small) is

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

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MediumAIIMS 2011

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With a standard rectangular bar magnet, the time period of a vibration magnetometer is $4 \,s$. The bar magnet is cut parallel to its length into four equal pieces. The time period of the vibration magnetometer when one piece is used (in seconds) (bar magnet breadth is small) is

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Two bar magnets $A$ and $B$ are geometrically similar but the magnetic moment of $A$ is twice that of $B$. $T_1$ is the time period of oscillation when their like poles are kept together. When unlike poles are kept together,the time period of oscillation is $T_2$. The ratio $T_1: T_2$ will be

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 \ Hz$ when like poles are tied together and it is $2 \ Hz$ when the unlike poles are tied together, then the ratio $M_1: M_2$ is

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