Q. The time of vibration of a dip needle vibrating in the vertical plane is 3s. When magnetic needle is made to vibrate in the horizontal plane, the time of vibration is $3\sqrt{2}$s. Then the angle of dip is
A) $30{^\circ}$
B) 45${^\circ}$
C) 60${^\circ}$
D) 90${^\circ}$
Explanation
(c) $t_{1} = 3 = 2\pi\sqrt{\frac{I}{MR}},$ where $R$ resultant intensity of earth’s field.
$t_{2} = 3\sqrt{2} = 2\pi\sqrt{\frac{I}{MH}}$
Divide $\frac{1}{\sqrt{2}} = \sqrt{\frac{H}{R}} = \sqrt{\frac{R\cos\delta}{R}} = \sqrt{\cos\delta}$
$\cos\delta = \frac{1}{2},\delta = 60{^\circ}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.