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

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles