Question

A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a plane where dip angle is $30^{\circ }$ and 15 oscillations per minute at a place where dip angle is $60^{\circ }$. The ratio of earth's magnetic fields at two places is

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

Answer 1

Answer: (B)

Time period of suspended magnet $T=2\pi \sqrt{\frac{i}{MB\cos \delta }}$ $v=\frac{1}{2\pi }\sqrt{\frac{MB\cos \delta }{i}}$ $v\propto \sqrt{B\cos \delta }$ or $B\propto \frac{v^2}{\cos \delta }$ $\therefore \frac{B_1}{B_2}=\frac{400}{\cos 30^{\circ }}\times \frac{\cos 30^{\circ }}{225}$ $=\frac{16\times 2}{9\times \sqrt{3}}\times \frac{1}{2}=16:9\sqrt{3}$