Two small balls,A and B,attract each other gravitationally with a force of magnitude F.If we now double both masses and the separation of the balls,what will now be the magnitude of the attractive force on each one?
A)16F
B)8F
C)4F
D)F
E)F/4

Question

Quizplus · Accepted Answer

The gravitational force between two masses 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, and $r$ is the separation between the centers of the two masses. If both masses are doubled ($2m_1$ and $2m_2$) and the separation is also doubled ($2r$), the new force $F'$ can be calculated as $F' = G\frac{(2m_1)(2m_2)}{(2r)^2}$. Simplifying this gives $F' = G\frac{4m_1m_2}{4r^2} = G\frac{m_1m_2}{r^2} = F$, meaning the force remains the same.

Two Small Balls,A and B,attract Each Other Gravitationally with a Force