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

Options

A. `2sqrt3s`
B. `(2)/(3)s`
C. `2s`
D. `(2)/(sqrt3)s`

Answer

b

Explanation

(b) `T=2pisqrt((I)/(MxxB))=2pisqrt((I)/(MB))` 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))xx3=(I)/(9)`
We have, Magnetic moment (M)=Pole strength (m)`xxl`
`therefore` New magnetic moment,
`M.=mxx((l)/(3))xx3=ml=M therefore T. =(T)/(sqrt9)=(2)/(3)s`.