A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a place where dip angle is `30^(@)` and 15 oscillations minute at a place where dip angle is `60^(@)`. The ratio of total earth's magnetic field at the two places is

Options

A. `3sqrt(3):8`
B. `16:27`
C. `4:9`
D. `2sqrt(3):9`

Answer

B

Explanation

`H_(1)=B_(1) cos 30^(@), H_(2)=B_(2) cos 60^(@)`
`T=2pisqrt(I/(MH))`
`T_(1)=2pisqrt(I/(MB_(1) cos 30^(@)))`
and `T_(2)=2pisqrt(I/(MB_(2) cos 60^(@)))`
`T_(2)/T_(1)=sqrt((B_(1) cos 30^(@))/(B_(2) cos 60^(@)))implies4/3=sqrt(B_(1)/B_(2))xxsqrt(3)`
`4/3=sqrt(B_(1)/B_(2))xxsqrt(3)`
`:. B_(1)/B_(2)=16/(9(3))=16/27`