Question

1. if the distance between two planets doubles, the force of gravity between them (a) doubles (b) quadruples (c) decreases to half (d) decreases to one - quarter

Explanation:

Step1: Recall gravitational - force formula

The gravitational force between two objects is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ 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 change when $r$ doubles

Let the initial distance be $r_1 = r$ and the new distance be $r_2=2r$. The initial force is $F_1 = G\frac{m_1m_2}{r^2}$, and the new force $F_2 = G\frac{m_1m_2}{(2r)^2}=G\frac{m_1m_2}{4r^2}$.

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

$\frac{F_2}{F_1}=\frac{G\frac{m_1m_2}{4r^2}}{G\frac{m_1m_2}{r^2}}=\frac{1}{4}$, which means $F_2=\frac{1}{4}F_1$.

Answer:

(d) decreases to one - quarter