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Question

With a standard rectangular bar magnet of length l, breadth b(b<<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
16
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B
2
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C
1
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D
0.25
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Solution

The correct option is B 1
Time period of vibration: TIM where I is the moment of inertia and M is the magnetic moment T1T2=I1M2I2M1
When the magnet is broken into 4 pieces, magnetic moment becomes 14th
M1=4M2
Moment of inertial also changes.
I1=ml212
I2=m4(l4)212
T1T2=I1M2I2×4M2=1×644=4
T2=T1×14=44=1s

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