Question

A dip needle lies initially in the magnetic meridian when it shows an angle of $dip\theta$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of $dip{\theta }^{\prime }$. Then, $\frac{\tan {\theta }^{{}^{\prime }}}{\tan \theta }$ will be

• A. $\cos x$
• B. $\frac{1}{\cos x}$
• C. $\frac{1}{\sin x}$
• D. $\frac{1}{\tan x}$

Answer 1

The correct option is B $\frac{1}{\cos x}$

In first case
$\tan \theta =\frac{B_V}{B_H}...\left(i\right)$
In second case
$\tan {\theta }^{\prime }=\frac{B_V}{B_H\cos x}...\left(ii\right)$
From Eqs (i) and (ii) we get
$\frac{\tan {\theta }^{\prime }}{\tan \theta }=\frac{1}{\cos x}$