Question

Two objects have masses of `32 MG` and `23 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `7 m` to `34 m`?

Answer 1

I will assume by "MG" you mean megagrams, notated `"Mg"`. The gravitational force between objects of masses of the magnitude of `10^-3` is very negligible. If my assumption is false merely follow my method!

Recall,

`F_"G" = G * (m_1m_2)/r^2`

By extension, the gravitational force is inversely proportional to the square of the distance between the bodies, such that,

`F_"G" propto 1/r^2`

Given,

`m_1 = 32"Mg"`, and `m_2 = 23"Mg"`

`r_1 = 7"m"`, and `r_2=34"m"`

Hence,

`DeltaF_"G" = Gm_1m_2(1/r_1^2 - 1/r_2^2) approx 960"N"`

is the difference in gravitational force between the objects as a function of increasing radius.