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

Explanation

In horizontal plane ,frequency of oscillation is ,`f=1/2pi sqrt(MB_(B)/I=sqrt(1/2pi sqrt(MBcos phi/I)`
Using above relation ,we can derive
`f_(1)/f_(2)=sqrt(B_(1)cos 30/B_(2)cos 60)=sqrt(B_(1)sqrt(3)/B_(2))`
Squaring both sides `(20/15)^(2)=B_(1)sqrt(3)/B_(2)`
Solving we gwt ,`B_(1)/B_(2)=16/9sqrt(3)`