Question

Two objects have masses of `9 MG` and `5 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `36 m` to `48 m`?

Answer 1

`GM_1M_2(\frac{1}{D_1}-1/D_2)`

Explanation:

Hint: In general, the gravitational potential energy `U` of two point masses `M_1` & `M_2` at a distance `D` between them is given as

`U=-\frac{GM_1M_2}{D}`

Hence, if the distance between the masses changes from `D_1` to `D_2` such that `D_2>D_1` then the change in gravitational potential energy `\Delta U` is given as follows

`\Delta U=U_2-U_1`

`=-\frac{GM_1M_2}{D_2}-(-\frac{GM_1M_2}{D_1}_`

`=GM_1M_2(\frac{1}{D_1}-1/D_2)`