A bar magnet of magnetic moment M and moment | vedclass

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(A) The time period of a bar magnet oscillating in a magnetic field $B$ is given by $T = 2 \pi \sqrt{\frac{I}{MB}}$.For the original magnet,$I = \frac

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$T/2$

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(A) The time period of a bar magnet oscillating in a magnetic field $B$ is given by $T = 2 \pi \sqrt{\frac{I}{MB}}$.For the original magnet,$I = \frac{m l^2}{12}$,where $m$ is the mass and $l$ is the length.When the magnet is cut into two equal pieces perpendicular to its length,the length of each piece becomes $l' = l/2$ and the mass becomes $m' = m/2$.The new moment of inertia $I'$ for each piece about its center is $I' = \frac{m' (l')^2}{12} = \frac{(m/2) (l/2)^2}{12} = \frac{m l^2}{12 	imes 8} = \frac{I}{8}$.The new magnetic moment $M'$ for each piece is $M' = M/2$.The new time period $T'$ is $T' = 2 \pi \sqrt{\frac{I'}{M' B}} = 2 \pi \sqrt{\frac{I/8}{(M/2) B}} = 2 \pi \sqrt{\frac{1}{4} \frac{I}{MB}} = \frac{1}{2} \left( 2 \pi \sqrt{\frac{I}{MB}} ight) = \frac{T}{2}$.

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