The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is T. The magnet is cut along its length into six parts and these parts are then placed togather as shown in the figure. The time period of this combination will be

Options

A. `T`
B. `T/sqrt(3)`
C. `T/(2sqrt(3))`
D. Zero

Answer

C

Explanation

`T=2pisqrt(I/(MH))`, `M` of each part `=I/6^(3)`
and magnetic moment of each part `=M/6`
so net `MI` of system `=I/6^(3)xx6=I/6^(2)`
and net magnetic moment `=(4M)/6-(2M)/6=M/3`
`:.` Time period of the system,
`T^(')sqrt((I//6^(2))/((M//3)H))=T/sqrt(12)=T/(2sqrt(3))`