Question

Two objects have masses of `27 MG` and `42 MG`. How much does the gravitational potential energy between the objects change if the distance between them changes from `54 m` to `32 m`?

Answer 1

It increases by `85.0%`

Explanation:

`F = G(m_1m_2/)r^2`
where G is the gravitational constant (`6.67 xx 10^(-11) m^3 s^(-2) kg^(-1))`, r is the distance between the two objects, and F is the magnitude of the force between the objects.

So, the change is inversely proportional to the square of the distance change for the same masses.
`DeltaF = Delta(1/r^2)` for the same masses.

`DeltaF = (1/54^2) – (1/32^2) = 0.0003429 – 0.0009766 = -0.0006344`
A increase of `(0.0006344 – 0.0003429)/0.0003429 xx 100 = 85.0%`