The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is ` 2 s`. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together . The time period of this combination will be
A
`2 sqrt(3) s`
B
` (2)/(3) s`
C
`2 s`
D
`(2)/sqrt(3) s`
Text Solution
Verified by Experts
The correct Answer is:
B
`T = 2pi sqrt(I)/(mxxB) where I = (1)/(12)ml^(2)` When the magnet is cut into three pieces the pole strength will remain the same and `M.I.(I') = (1)/(12) ((m)/(3)) ((l)/(3))^(2) xx 3 = (I)/(9)` We have , `Magnetic moment(M) = Pole strength(m)xl` :. New magnetic moment, `M' = mxx((l)/(3))xx3 = ml = M :. T' = (T)/(sqrt(9)) = (2)/(3) s`.
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