A magnet is cut in three equal parts by cutting it perpendicular to its length. The time period of original magnet is `T_0` in a uniform magnetic field B. Then, the time period of each part in the same magnetic field is

Options

A. `T_0/2`
B. `T_0/3`
C. `T_0/4`
D. none of these

Answer

B

Explanation

For original magnet, `T_0=2pisqrt((I)/(MB))` …(i)
When a magnet is cut into three equal parts, perpendicular to its length, then magnetic moment of each part is `M^'=M//3`. Moment of inertia of each part is
`I^'=m/3xx((L//3)^2)/(12)=(1)/(27)xx(mL^2)/(12)=(I)/(27)`
`:.` New time period, `T^'=2pisqrt((I^')/(M^'B))`
`=2pisqrt((I//27)/((M//3)B))=1/32pisqrt((I)/(MB))=T_0/3`