question_answer

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\[\theta \]. Then, \[\frac{\tan \theta }{\tan \theta }\]will be

A)  \[\cos x\]

B)  \[\frac{1}{\cos x}\]

C)  \[\frac{1}{\sin x}\]

D)  \[\frac{1}{\tan x}\]

Correct Answer: B

Solution :

 In first case, \[\tan \theta =\frac{{{B}_{V}}}{{{B}_{H}}}\] ?(i) In second case, \[\tan \theta =\frac{{{B}_{V}}}{{{B}_{H}}\cos x}\] ?(ii) From Eqs,(i) and (ii), we get \[\frac{\tan \theta }{\tan \theta }=\frac{1}{\cos x}\]