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. $1/3$
• C. $\sqrt{3}$
• D. $1/\sqrt{3}$

Answer 1

Answer: (B)

$1/3$

According to the question, $T\propto \frac{1}{\sqrt{H}}\Rightarrow \frac{T_1}{T_2}=\sqrt{\frac{H_2}{H_1}}\Rightarrow \frac{2}{1}=\sqrt{\frac{H+F}{H}}\Rightarrow F=3H$

or $\frac{H}{F}=\frac{1}{3}$