Question

Two objects attract each other gravitationally. If the distance between their centers increases by a factor of 3, and both of the objects' masses increase by the same factor, how does the gravitational force between them change? A) The gravitational force decreases by a factor of 3.

B) The gravitational force increases by a factor of 3.
C) The gravitational force decreases by a factor of 9.
D) The gravitational force increases by a factor of 9.
E) The gravitational force remains unchanged.

Answer 1

E. The gravitational force remains unchanged

Step-by-step explanation:

Answer 2

E

Step-by-step explanation:

F = G * m1 * m2 / r^2 Increase the distance by 3

F1 = G * m1 * m2 / (3r)^2

F1 = G * m1 * m2 / (9*r^2) What this means is the the force decreases by a factor of 9, but we are not done.

F2 = G * 3m1 * 3m2 / (9 r^2)

F2 = G * 9 m1 * m2 / (9 r^2)

In F2 the 9s cancel out and we are left with

F2 = G * m1 * m2/r^2 which is the same thing.

F2 equals F