Question

The angle of the dip, if a dip needle oscillating in a vertical plane makes 40 oscillations per minute in a magnetic meridian and 30 oscillations per minute in a vertical plane at right angle to the magnetic meridian, is:

• A. $\theta ={\tan }^{-1}\left(0.5625\right)$
• B. $\theta ={\sin }^{-1}\left(0.325\right)$
• C. $\theta ={\sin }^{-1}\left(0.425\right)$
• D. $\theta ={\sin }^{-1}\left(0.235\right)$

Answer 1

The correct option is A $\theta ={\tan }^{-1}\left(0.5625\right)$

We have,
${\omega }_{\nu }=40/min$

${\omega }_H=30/min$

We know that, $\tan \theta ={\left(\frac{{\omega }_H}{{\omega }_{\nu }}\right)}^2$

$\tan \theta ={\left(\frac{30}{40}\right)}^2$

$\theta ={\tan }^{-1}{\left(0.75\right)}^2$

$\theta ={\tan }^{-1}\left(0.5625\right)$