Question

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 which of the following compared with the gravitational force exerted by the planet on Moon 1?
half as largetwice as largeone-fourth as largefour times as largethe same

Answer 1

Answer:

Half as large.

Explanation:

Using Newton's law of universal gravitation, if the mass of the planet is M and of the Moons 1 and 2 is m, them the force exerted by the planet on them will be:

$F_1=\frac{GMm}{r}$

$F_2=\frac{GMm}{2r}$

Which clearly shows that the force that the planet exerts on the Moon 2 is half  the force it exerts on the Moon 1.