The diagram shown represents two satellites, A and B, of equal mass in circular orbits around a planet. The magnitude of the gravitational force of attraction between satellite B and the planet is _____ as great as the magnitude of the gravitational force of attraction between satellite A and the planet.
a) three times
b) one-ninth
c) nine times
d) one-third
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Explanation:
From Newton's law of Gravitationa,
Force ( F ) is inversely proportional to square of the distance ( R ) between two objects,
That is,
F ∝ 1 / R²
Given,
R = 3R
R² = ( 3R )² = 9R²
F ∝ 1 / 9 R²
F = 1 / 9 ( or ) one - ninth
Therefore, The magnitude of the gravitational force of attraction between satellite B and the planet is one - ninth as great as the magnitude of the gravitational force of attraction between satellite A and the planet.
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