Two bar magnets of the same length and breadth but having magnetic moments `M` and `2M` are joined with like poles together and suspended by a string. The time of oscillation of this assembly in a magnetic field of strength `B` is `3` sec. What will be the period of oscillation, if the polarity of one of the magnets is changed and the combination is again made to oscillate in the same field ?

Explanation

As magnetic moment is a vector, so when magnets are joined with like poles together `M_(1)=M+2M=3M`, so
`T=2pisqrt(((I_(1)+I_(2)))/(3MB))" ".....(1)`
When the polarity of one of the magnets is reversed,
`M_(2)=M~2M=M`,
so `T.=2pisqrt(((I_(1)+I_(2)))/(MB))" ".....(2)`
Dividing Eq. (2) by (1),
`(T.)/T=sqrt3," "i.e.,T.=(sqrt3)T=3sqrt3sec`