Question

In a vibration magnetometer, the time period of a bar magnet oscillating in horizontal component of earth's magnetic field is 2 sec. When a magnet is brought near and parallel to it, the time period reduces to 1 sec. The ratio H/F of the horizontal component H and the field F due to magnet will be

• A. $3$
• B. $\frac{1}{3}$
• C. $\sqrt{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is B $\frac{1}{3}$

$T\propto \frac{1}{\sqrt{H}}\Rightarrow \frac{T_1}{T_2}=\sqrt{\frac{H_2}{H_1}}\Rightarrow \frac{2}{1}=\sqrt{\frac{H+F}{H}}\Rightarrow F=3H$
or $\frac{H}{F}=\frac{1}{3}$