Two small objects,with masses m and M,are originally a distance r apart,and the gravitational force that they exert on each other 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)F/32
B)F/16
C)16F
D)32F
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 $16F$.

Two Small Objects,with Masses M and M,are Originally a Distance