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. `2 s`
B. `2//3 s`
C. `2sqrt(3)s`
D. `2//sqrt(3)s`

Answer

B

Explanation

Initially the time period of the magnet
`T=2=2pisqrt(I/(MB)) …(i)`
For each part, its moment of inertia=`I/27` and magnetic moment=`M/3`
:. Moment of intertia of system `M_(s)=M/3xx3=M`
Time period of system
`T_(s)=2pisqrt(I_(s)/(M_(s)B))=1/3xx2pisqrt(I/(MB))=T/3=2/3 sec`