Two small balls,A and B,attract each other gravitationally,exerting a force of magnitude F on each other.If we now double both masses and the separation of the balls,what will now be the magnitude of the attractive force that they exert 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 masses. Doubling both masses would increase the force by a factor of 4 (since both $m_1$ and $m_2$ are doubled, the product $m_1m_2$ becomes 4 times larger). Doubling the separation would decrease the force by a factor of 4 (since the force is inversely proportional to the square of the separation, doubling $r$ would increase $r^2$ by a factor of 4, thus reducing the force by the same factor). Therefore, the changes cancel each other out, and the force remains $F$.

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