AIIMS 2017 Physics Magnetic Dip MCQ Question

The angle of dip (θ) can be determined using the formula $\tan(θ) = \frac{N_1^2 - N_2^2}{2N_2^2}$, where $N_1$ is the number of oscillations in the magnetic meridian (40 oscillations/min) and $N_2$ is the number of oscillations at right angles to it (30 oscillations/min). Substituting these values gives $\tan(θ) = \frac{40^2 - 30^2}{2 \times 30^2} = \frac{1600 - 900}{1800} = \frac{700}{1800} = \frac{7}{18}$, leading to $θ = \sin^{-1}(0.5625)$.

Other options are incorrect because they correspond to different values of $\tan(θ)$ that do not match the calculated ratio, thus not representing the angle of dip based on the observed oscillation frequencies.