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

Options

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

Answer

3

Explanation

`T alpha 1/sqrt(B_(H))=/sqrt(Bcos phi) rArr T_(1)/T_(2)=sqrt(B_(2)cos phi_(2)/B_(2)cos phi(1))`
`rArr B_(1)/B_(2)=T_(2)^(2)/T_(1)^(2) xx cos phi_(2)/cos phi_(1)=(3/2)^(2) xx cos60/cos30 rArr B_(1)/B_(2)=9/4sqrt(3)`