A planet has mass m1 and is at a distance r, from the sun. A...

JAMB 1997

A planet has mass m₁ and is at a distance r, from the sun. A second planet has mass m₂ = 10m₁ and at a distance of r₂ = 2r₁ from the sun. Determine the ratio of the gravitational force experienced by the planets.

A. 1 : 5
B. 2 : 5
C. 3 : 5
D. 4 : 5

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Correct Answer: Option B

Explanation

g = \(\frac{GM}{R^2}\)

\(\frac{G_1M_1}{r^2_1}\) = \(\frac{G_2M_2}{r^2_2}\)

\(\frac{G_1M_1}{r^2_1}\) = \(\frac{G_2 {\times}10 M_1}{(2r_1)^2}\)

\(\frac{G_1}{G_2}\) = \(\frac{2}{5}\)

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