Question

question 9 of 24 how does the gravitational force between two objects change if the distance between the objects is doubled? a. the gravitational force decreases by a factor of 4. b. the gravitational force increases by a factor of 4. c. the gravitational force decreases by half. d. the gravitational force doubles.

Explanation:

Step1: Original gravitational force formula

\( F_{\text{original}} = G \frac{m_1 m_2}{r^2} \)

Step2: New force with doubled distance (\( r' = 2r \))

\( F_{\text{new}} = G \frac{m_1 m_2}{(2r)^2} = \frac{1}{4} F_{\text{original}} \)

Answer:

A. The gravitational force decreases by a factor of 4.