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Take the mean distance of the moon and the sun from the earth to be 0.4×10⁶ km and 150×10⁶ km respectively. Their masses are 8×10²² kg and 2×10³⁰ kg respectively. The radius of the earth is 6400 km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. The number closest to ΔF1/ΔF2 is:

1. 2
2. 6
3. 10⁻²
4. 0.5

Correct answer: 2

Solution

The near-far force difference (tidal effect) scales as M/d^3. Ratio = (M_moon/d_moon^3)/(M_sun/d_sun^3) = (8e22/(0.4e6)^3)/(2e30/(150e6)^3) ≈ 2.1, so the closest number is 2.

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