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) F
B) 16 F
C) F/4
D) 4 F
E) 8 F

Question

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)  F 
B)  16 F 
C)  F/4
D)  4 F 
E)  8 F

Quizplus · Accepted Answer

Doubling both masses increases the force by a factor of 4 (since gravitational force is proportional to the product of the masses), but doubling the separation decreases the force by a factor of 4 (since gravitational force is inversely proportional to the square of the separation distance). These changes cancel out, leaving the force unchanged at F.

Two Small Balls, a and B, Attract Each Other Gravitationally