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.

E

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

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.