A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B_1 and…

A magnetic compass needle oscillates $\displaystyle 30$ times per minute at a place where the dip is $\displaystyle 45$°, and $\displaystyle 40$ times per minute where the dip is $\displaystyle 30$°. If $\displaystyle \mathrm{B}_1$ and $\displaystyle \mathrm{B}_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $\displaystyle B_1 / B_2$ is best given by :