   Chapter 7.5, Problem 7.9QQ

Chapter
Section
Textbook Problem

A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) four times as large (b) twice as large (c) the same (d) half as large (e) one-fourth as large as the gravitational force exerted by the planet on Moon 1.

To determine
The magnitude of the gravitational force exerted by the planet on moon 2.

Explanation

Given Info: The radius of the circular orbit of the moon 1 is r and radius of the circular orbit of the moon 2 is 2r

Explanation:

Formula to calculate the gravitational force is,

Fg=GMmr2

• G is the gravitational constant
• M is the mass of the planet
• m is the mass of moon
• r is the radius of the circular orbit

Since, the gravitational force is inversely proportional to the square of radius of the circular orbit and the radius of the orbit of moon 2 is twice the radius of orbit of moon1; the gravitational force on the moon 2 exerted by the planet will be one-fourth of the gravitational force exerted by the planet on the moon1

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