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. `16:9sqrt(3)`
C. `4:9`
D. `2sqrt(2):3`

Answer

B

Explanation

`T=2pisqrt(I/(MB cos delta))impliesv=1/(2pi)sqrt((MB cos delta)/I )`
`v=sqrt(B cos delta) or Bpropv^(2)/(cos delta)`
`B_(1)/B_(2)=400/(cos 30^(@))xx(cos 60^(@))/225=(16xx2)/(9xxsqrt(3))xx1/2 16:9sqrt(3)`