Question

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

• A. $0^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${45}^o$

Time period $t_1=2=2\pi \sqrt{\frac{l}{MV}}$
Similarly, $t_1=2=2\pi \sqrt{\frac{l}{MH}}$
where $I=$ moment of inertia of needle, $M=$ magnetic moment of needle and $V$ and $H$ are vertical and horizontal components of Earth's magnetic field
$V=H\tan \delta =\frac{V}{H}=1$,
$\delta ={45}^o$