Question

If the distance between two objects is increased by a factor of 6, how will this affect Fg?

it will increase by 6 times
it will increase by 24 times
it will decrease to 1/18
it will decrease to 1/36

Answer 1

\(\color{black}{\displaystyle F_{\rm grav}=G\cdot \frac{m_1m_2}{d^2} }\)

Answer 2

so it will decrease to 1/18??

Answer 3

If you make the distance between \(m_1\) and \(m_2\), \(k\) times bigger, you get:
\(\color{black}{\displaystyle G\cdot \frac{m_1m_2}{(kd)^2}=G\cdot \frac{m_1m_2}{k^2d^2} =\frac{1}{k^2}\cdot G\cdot \frac{m_1m_2}{d^2} =\frac{1}{k^2}\cdot F_{\rm grav} }\)

Answer 4

So, (just as I derived), if you increase the distance between the two objects by a factor of \(k\), then the force \(F_g\) will be \(1/k^2\) greater (or \(k^2\) times smaller).

Answer 5

so 1/36 right?

Answer 6

Your choices are worded improperly.
The distance decreasing to 1/36 is not the same as the distance becoming 36 times smaller.

Answer 7

However, your original \(F_g\) is \(36\) times smaller (or \(1/36\) times greater), that is correct.

Answer 8

that is the exact way they are worded in my homework

Answer 9

Sure, why not. (I didn't claim otherwise.)

Answer 10

Well, it's 1/36 times greater.
(Their wording is inaccurate, so I don't really want to say D is right.)

Answer 11

but, for trivial purposes, just go with D.