With a standard rectangular bar magnet of length (l), breadth (b,bltlt) 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 second) with one of the piece is

Options

A. 16
B. 2
C. 1
D. `4`

Answer

C

Explanation

Time period of vibration magnetometer, `T=2pisqrt((I)/(MB_(H))`
When the magnet is made into n equal parts normal to its length, then,
Moment of inertia=`(I)/(n^(3))`
Magnetic moment= `M/n`
`T=2pisqrt((I/n^(3))/(M/(nB_(H))))=T/n=4/4`=is