A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be 2 second…

Q: A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be 2 second. The same needle is then allowed to vibrate in the horizontal plane, and the time period is again found to be 2 seconds. Then the angle of dip is

(a) 0°

(b) 30°

(c) 45°

(d) 90°

Ans: (c)

Sol: $\displaystyle t_1 = 2\pi \sqrt{\frac{I}{M B_V}}$

$ \displaystyle 2 = 2\pi \sqrt{\frac{I}{M B_V}}$

$ \displaystyle t_2 = 2\pi \sqrt{\frac{I}{M B_H}}$

$ \displaystyle 2 = 2\pi \sqrt{\frac{I}{M B_H}}$

$ \displaystyle B_V = B_H $

$\displaystyle tan\delta = \frac{B_V}{B_H} = 1 $

δ = 45°

Author: Rajesh Jha

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