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  4. A magnetic compass needle oscillates 30 times per sec at a place where the dip angle is 45° , and 40 times per second where the dip angle is 30o . If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio B1/B2 is nearly equal to :

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Q. A magnetic compass needle oscillates $30$ times per sec at a place where the dip angle is $45^\circ ,$ and $40$ times per second where the dip angle is $30^{o}$ . If $B_{1}$ and $B_{2}$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_{1}/B_{2}$ is nearly equal to :

NTA AbhyasNTA Abhyas 2020

Solution:

$n=\frac{1}{2 \pi }\sqrt{\frac{M B_{H}}{1}}$
$B_{H}=B_{e}cos\phi$
$\frac{n_{1}}{n_{2}}=\sqrt{\frac{B_{1} cos \phi_{1}}{B_{2} cos \phi_{2}}}$
$\frac{30}{40}=\sqrt{\frac{B_{1} cos 45 ^\circ }{B_{2} cos 30 ^\circ }}$
$=\frac{9}{16}\times \frac{\sqrt{6}}{2}=0.68$