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. `4/(4sqrt(3))`
D. `9/sqrt(3)`

Answer

C

Explanation

`T prop 1/sqrt(B_(H))=1/sqrt(B cos varphi)implies T_(1)/T_(2)=sqrt((B_(2) cos varphi_(2))/(B_(2) cos varphi_(1)))`
`impliesB_(1)/B_(2)=T_(2)^(2)/T_(1)^(2)xx(cos varphi_(2))/(cos varphi_(1))=(3/2)^(2)xx(cos 60)/(cos 30)implies B_(1)/B_(2)=9/(4sqrt(3))`