Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the
Distance is changed to r/4. What is the magnitude of the new gravitational force?
A) 16F
B) 32F
C) F/16
D) F/32
E) 2F

Question

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, and $r$ is the distance between the centers of the two masses. When the mass of the second object is doubled to $2M$ and the distance is reduced to $r/4$, the new force $F'$ can be calculated as $F' = G\frac{m(2M)}{(r/4)^2} = G\frac{2mM}{r^2/16} = 16G\frac{mM}{r^2}$, which is $16$ times the original force $F$.

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