Question

A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a place where dip angle is 30${}^0$ and 15 oscillations per minute at a place where dip angle is 60${}^0$. Ratio of the total earths magnetic field at the two places is :

• A. $3\sqrt{3}:8$
• B. $16:9\sqrt{3}$
• C. $4:9$
• D. $2\sqrt{3}:9$

Answer 1

The correct option is B $16:9\sqrt{3}$

At first place , horizontal component of earth's magnetic field is given by
$B_{h1}=B_{1}cos30=\frac{\sqrt{3}{B}_1}{2}$
$B_{h2}=B_{2}cos60=\frac{B_2}{2}$
$\frac{f_1^2}{f_2^2}=\frac{B_{h1}}{B_{h2}}$
$\frac{16}{9}=\frac{\sqrt{3}{B}_1}{B_2}$
$\frac{B_1}{B_2}=\frac{16}{9\sqrt{3}}$