A magnet oscillating in a horizontal plane has a time period of 2 seconds at a place where the angle of dip is `30^(@)` and 3 seconds at another place where the angle of dip is `60^(@)`. The retio of resultant magnetic field at the two places is

Options

A. `(4sqrt(3))/7`
B. `4/(9sqrt(3))`
C. `9/(4sqrt(3))`
D. `9/(sqrt(3))`

Answer

C

Explanation

`Tprop1/sqrt(B_(H))=1/sqrt(B cos phi)impliesT_(1)/T_(2)=sqrt((B_(2) cos phi_(2))/(B_(2) cos phi_(1)))`
`implies B_(1)/B_(2)=T_(2)^(2)/T_(1)^(2)xx(cos phi_(2))/(cosphi_(1))=(3/2)^(2)xx(cos 60)/(cos 30)`
`implies B_(1)/B_(2)=9/(4sqrt(3))`