Question

what happens to the gravitational force between two objects if the distance between them triples? (1 point)
the force decreases by a factor of 3.
the force decreases by a factor of 9.
the force increases by a factor of 9.
the force increases by a factor of 3.

Explanation:

Step1: Recall Newton's law of gravitation

Newton's law of gravitation is given by \(F = \frac{Gm_1m_2}{r^2}\), where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them.

Step2: Analyze the effect of tripling the distance

Let the initial distance be \(r\) and the initial force be \(F_1=\frac{Gm_1m_2}{r^2}\). When the distance triples, the new distance \(r_2 = 3r\). The new force \(F_2=\frac{Gm_1m_2}{(3r)^2}=\frac{Gm_1m_2}{9r^2}\).

Step3: Find the ratio of the new force to the initial force

\(\frac{F_2}{F_1}=\frac{\frac{Gm_1m_2}{9r^2}}{\frac{Gm_1m_2}{r^2}}=\frac{1}{9}\)

Answer:

The force decreases by a factor of 9.