Question

Consider the law of gravitational attraction. Two spheres with a mass, M, are attracted to each other by a force, F. If the distance between the two spheres doubles while the masses remain constant, will the force between the two spheres change? If yes, how?
A)
Yes, the force decreases by 1/4.
B)
Yes. The force decreases by 1/2.
C)
Yes, the forces decreases by 1/16.
D)
No. The force remains constant because the masses remain constant.

Answer 1

PLEASE HELP IM ABOUT TO FAIL MY TEST AGAIN

Answer 2

I have no clue what the answer is

Answer 3

Use the equation
\[\huge F_\text{G}=G\frac{m_1m_2}{r^2}\]

Answer 4

What can you see about the relationship between the distance between and the force?

Answer 5

Im so sorry, but I dont understand :(

Answer 6

I feel so stupid

Answer 7

There is an inverse relationship between the force and the distance squared. That is,
\[\huge F_G \propto \frac{1}{r^2}\]
Whenever we make changes to one thing, we have to re-equalize our relationship. From our initial equation we can see that all the coefficients are 1. Our goal is to keep it that way!

Now we're told that our radius is doubled, so if we replace 2r with r, we get
\[\huge F_\text{G}=G\frac{m_1m_2}{(2r)^2}=G\frac{m_1m_2}{4r^2}\]

Now what must we multiply the left side (the F) by in order to maintain our coefficients to be 1?

Answer 8

1/4 ?

Answer 9

Yep!! So that's what happens to our force. If we double the distance between two masses, the force is reduced by a factor of 1/4

Answer 10

Thanks so much!!!!

Answer 11

No problem X)