A thin magnetic iron rod of length 30 cm is suspended in a uniform magnetic field. Its time period of oscillation is 4s. It is broken into three equal parts. The time period in second of oscillation of one part. When suspended in the same magnetic field, is

Options

A. `1/sqrt(3)`
B. `2/sqrt(3)`
C. `sqrt(3)`
D. `4/sqrt(3)`

Answer

A

Explanation

`T=2pisqrt(I/(MH))`
Where `I=(mL^(2))/12=` moment of inertia of thin magnetic rod.
When given rod is broken into three equal parts, then
`M^(')=M/9` and `I^(')=I/27=M.I.` of each piece.
`:. T^(')=2pisqrt(I^(')/(M^(')H))=2pisqrt((I9)/(27xxMH))=T/sqrt(3)`