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Q. A dip needle arranged to move freely in the magnetic meridian dips by an angle $\theta$. If the vertical plane in which the needle moves is rotated through an angle $\alpha$ to the magnetic meridian, then the needle will dip by an angle

BHUBHU 2008Magnetism and Matter

Solution:

In this question, $\cos \alpha<1$
i.e., $\frac{1}{\cos \alpha}>1$
or, $\frac{\tan \theta '}{\tan \theta}>1$
or, $\tan \theta ' > \tan \theta$
or, $\theta ' >\theta$
ie, angle of apparent dip is more than angle of actual dip $\theta$.