Question

Two objects have masses of `36 MG` and `18 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `81 m` to `27 m`?

Answer 1

`\Delta U = U_2 - U_1 = Gm_1m_2(1/d_1-1/d_2)= -1.07\times10^{-21}\quad J`

Explanation:

It is not clear what you mean by MG. It is a strange notation for a mass unit. It could mean Mega Grams which could easily be stated as `1000 \quad kg`.
So I assume you mean milli-grams by the symbol MG in solving this problem.

Gravitational Potential Energy: The Gravitational potential energy between two point masses `m_1` and `m_2` separated by a distance `d` is -

`U = -G\frac{m_1m_2}{d}`

The change in gravitational potential energy of the system when the distance changes for `d_1` to `d_2` is :

`\Delta U = U_2 - U_1 = Gm_1m_2(1/d_1-1/d_2)`

`G=6.67\times10^{-11}(Nm^2)/(kg^2); \qquad d_1 = 81\quad m; \qquad d_2=27\quad m;`
`m_1 = 36\times10^{-6}\quad kg; \qquad m_2 = 18\times10^{-6}\quad kg`

`\Delta U = -1.07\times10^{-21}\quad J`

The negative sign indicates that the potential energy decreases by that much. The sign makes sense because in attractive interactions the potential energy decreases if the objects are brought closer together.