At two places A and B using vibration magnetometer, a magnet vibr… - Vidyadip

MCQ

At two places $A$ and $B$ using vibration magnetometer, a magnet vibrates in a horizontal plane and its respective periodic time are $2$ sec and $3 \mathrm{sec}$ and at these places the earth's horizontal components are $H$ and $H$ respectively. Then the ratio between $H$ and $H$ will be

✓
$9: 4$
B
$3: 2$
C
$4: 9$
D
$2: 3$

✓

Answer

Correct option: A.

$9: 4$

$T=2 \pi \sqrt{\frac{I}{M H}} \Rightarrow T \propto \frac{1}{\sqrt{H}} \Rightarrow \frac{T_A}{T_B}=\sqrt{\frac{H_B}{H_A}}$
$ \Rightarrow \frac{H_A}{H_B}=\left(\frac{T_B}{T_A}\right)^2=\left(\frac{3}{2}\right)^2=\frac{9}{4}$

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