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Question

A magnetic compass needle oscillates $$30$$ times per minute at a place where the dip is $$45^o$$, and $$40$$ times per minute where the dip 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 best given by :


A
2.2
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B
1.8
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C
0.7
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D
3.6
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Solution

The correct option is C $$0.7$$
$$f_1 = \dfrac{1}{2\pi} \sqrt{\dfrac{\mu B_1 \cos 45^o}{I}}$$
$$f_2 = \dfrac{1}{2\pi} \sqrt{\dfrac{\mu B_2\cos 30^o}{I}}$$
$$\dfrac{f_1}{f_2} = \sqrt{\dfrac{B_1 \cos 45^o}{B_2 \cos 30^o}}$$
$$\therefore \dfrac{B_1}{B_2} = 0.7$$
1248296_1615240_ans_f7cd7e093b234702b4dc5f8a987f792b.PNG

Physics

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