Q. At two places $A$ and $B$ using vibration magnetometer, a magnet vibrates in a horizontal plane and it respective periodic time are $2\ sec$ and $3\ sec$ and at these places the earth’s horizontal components are $H_{A}$ and $H_{B}$ respectively. Then the ratio between $H_{A}$ and $H_{B}$ will be
A) $9\ :4$
B) $3\ :2$
C) $4\ :9$
D) $2\ :3$
Explanation
(a) $T = 2\pi\sqrt{\frac{l}{MH}}\ \Rightarrow T \propto \frac{1}{\sqrt{H}} \Rightarrow \frac{T_{A}}{T_{B}} = \sqrt{\frac{H_{B}}{H_{A}}}$
$\Rightarrow \frac{H_{A}}{H_{B}} = \left( \frac{T_{B}}{T_{A}} \right)^{2} = \left( \frac{3}{2} \right)^{2} = \frac{9}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.