Question

Two particles of masses $m_1$ & $m_2$ are infinitely separated and their gravitational potential energy is chosen zero. Their gravitational energy, when they are separated by $r$, is

• A. $\frac{G{m}_1{m}_2}{r^2}$
• B. $\frac{G{m}_1{m}_2}{2r}$
• C. $\frac{-G{m}_1{m}_2}{r^2}$
• D. $\frac{G{m}_1{m}_2}{r}$

Answer 1

Answer: (D)

$\frac{G{m}_1{m}_2}{r}$

Potential energy is energy that is stored in a system.

In space, it is possible to find the potential energy of gravity between two objects separated by a distance.

since the force between them is attractive so work required will be negative.

so if initially they potential energy is zero, then when then distance is $r$ then potential energy will be $\frac{G{m}_1{m}_2}{r^2}$.

so best possible option is option D.

can be derived from the expression $F=-\frac{GMm}{r^2}$ and $-\frac{dP}{dr}=dF$