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 $\frac{\tan {\theta }^{\prime }}{\tan \theta }$ is

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

Answer 1

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

Here,
$\theta \to$Actual dip

${\theta }^{\prime }\to$ Apparent dip

$x\to$ Angle of plane with respect to the magnetic meridian.

Then, $\tan \theta =\frac{B_V}{B_H}......\left(1\right)$

$\tan {\theta }^{\prime }=\frac{B_V}{B_H\cos x}......\left(2\right)$

Dividing equation $\left(1\right)$ and $\left(2\right)$ we have,

$\Rightarrow \frac{\tan {\theta }^{\prime }}{\tan \theta }=\frac{1}{\cos x}$

Hence, option $\left(A\right)$ is the correct answer.