Two objects have masses of $6 M G$ $6 MG$ and $9 M G$ $9 MG$ . How much does the gravitational potential energy between the objects change if the distance between them changes from $300 m$ $300 m$ to $250 m$ $250 m$ ?

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Answer 1 · 2017-08-11T01:16:48

Gravitational potential energy is increased by 1.2 units,

Gravitational potential energy $(U) = - \frac{G M m}{r}$ $(U) = -(GMm)/r$

In both the cases GMm is same.

Hence we can say...,

$U \propto \frac{1}{r}$ $U ∝ 1/r$

$\frac{U_{1}}{U_{2}} = \frac{r_{2}}{r_{1}}$ $U_1/U_2 = r_2/r_1$

$\frac{U_{1}}{U_{2}} = \frac{250}{300}$ $U_1 /U_2 = 250/300$

$U_{2} = \frac{300 U_{1}}{250}$ $U_2 = (300U_1)/250$

$U_{2} = 1.2 U_{1}$ $U_2 = 1.2U_1$

Gravitational potential energy is increased by 1.2 units.

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