(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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Magnetism and Matter

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

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With a standard rectangular bar magnet of length $l$, breadth $b$ $(b \ll l)$ and magnetic moment $M$, the time period of the magnet in a vibration magnetometer is $4 \ s$. If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is

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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

Similar Questions

At a certain place,a magnet makes $30$ oscillations per minute. At another place,if the magnetic induction is increased to two times the magnetic induction at the first place,then the time period of the same magnet will be:

When two magnetic moments are compared using the equal distance method,the deflections produced are $45^\circ$ and $30^\circ$. If the lengths of the magnets are in the ratio $1:2$,the ratio of their pole strengths is:

With a standard rectangular bar magnet of length $l$, breadth $b$ $(b \ll l)$ and magnetic moment $M$, the time period of the magnet in a vibration magnetometer is $4 \ s$. If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is

$A$ short magnet oscillates with a frequency $10 \, Hz$ where the horizontal component of Earth's magnetic field is $12 \, \mu T$. $A$ downward current of $15 \, A$ is established in a vertical wire placed $20 \, cm$ west of the magnet. The new frequency of the magnet is (in $ \, Hz$)

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