Consider two planets in space that gravitationally attract each other. If the masses of both planets is doubled, and the distance between them is also doubled, then the force between them is
A)one-quarter.
B)half as much.
C)twice as much.
D)four times as much.
E)none of the above

Question

Quizplus · Accepted Answer

The gravitational force between two masses is given by Newton's law of gravitation, $F = G\frac{m_1m_2}{r^2}$, 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 their centers. If both masses are doubled ($m_1' = 2m_1$, $m_2' = 2m_2$) and the distance is also doubled ($r' = 2r$), the new force $F'$ can be calculated as $F' = G\frac{(2m_1)(2m_2)}{(2r)^2}$. Simplifying this gives $F' = G\frac{4m_1m_2}{4r^2} = G\frac{m_1m_2}{r^2} = F$. Therefore, the force remains unchanged, which is not listed among the options provided.

Consider Two Planets in Space That Gravitationally Attract Each Other