A thin magnetic iron rod of length 30 cm is suspended in a uniform magnetic field. Its time period of oscillation is 4 s. 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/sqrt3`
B. `2/sqrt3`
C. `sqrt3`
D. `4/sqrt3`

Answer

D

Explanation

Time period `T=2pisqrt((I)/(MB))=4S`
When the magnet is cut into 3 equal parts
Then, `M^(1)=M/3, I^(1)=(m(l/3)^(2))/(12)=(ml^(2))/(9xx12)=I/9`
Time period,
`T=2pisqrt((I^(1))/(MB))=2pisqrt((I/9)/(M/3B))=2pisqrt((I)/(MBxx3))`
`=T/sqrt3=4/sqrt3S`