Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is
Changed to 4r. What is the magnitude of the new gravitational force?
A) 16F
B) 4F
C) F/16
D) F/4
E) F/2

Question

Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is
Changed to 4r. What is the magnitude of the new gravitational force? 
A)  16F 
B)  4F 
C)  F/16 
D)  F/4 
E)  F/2

Quizplus · Accepted Answer

The gravitational force between two masses is given by $F = G\frac{mM}{r^2}$, where $G$ is the gravitational constant, $m$ and $M$ are the masses of the two objects, and $r$ is the distance between their centers. When the masses are changed to $2m$ and $2M$, and the distance is changed to $4r$, the new force $F'$ can be calculated as $F' = G\frac{(2m)(2M)}{(4r)^2}$. Simplifying this gives $F' = G\frac{4mM}{16r^2} = \frac{1}{4}G\frac{mM}{r^2} = \frac{1}{4}F$, so the magnitude of the new gravitational force is $F/4$.

Two Small Objects, with Masses M and M, Are Originally