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

Question

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.

Options

A) 1 : 5

B) 2 : 5

C) 3 : 5

D) 4 : 5

Related Lesson: Summarizing Satellites and Kepler’s Laws | Uniform Circular Motion and Gravitation

The correct answer is 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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  • Nigerian Scholars Follow4 years ago

    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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