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Compass needle oscillation counts at two places of different dip: ratio of total fields

The same question, asked 2 times: 27 Jul 2022*, 12 Apr 2023. Every wording below, oldest first.

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  1. Question 1

    27 Jul 2022

    102
    A compass needle of oscillation magnetometer oscillates 20 times per minute at a place PP of dip 30∘30^{\circ}. The number of oscillations per minute become 10 at another place QQ of 60∘dip60^{\circ}dip. The ratio of the total magnetic field at the two places (BQ:BP)\left( B_{Q}:B_{P} \right) is:

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  2. Question 2

    12 Apr 2023

    23
    A compass needle oscillates 20 times per minute at a place where the dip is 30∘30^{\circ} and 30 times per minute where the dip is 60∘60^{\circ}. The ratio of total magnetic field due to the earth at two place respectively is 4x\frac{4}{\sqrt{x}}. The value of xx is