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Classical Mechanics

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Moderate

Weird Gravity

CLMECH-TVEPKN

Suppose that the gravitational force was given by the equation:

$$F_G = -G\frac{m_1m_2}{r^3}$$

where G is the universal gravitational constant, $m_1$ is the mass of one object, $m_2$ is the mass of a second object, $r$ is the distance between their centers of mass, and $F_G$ is the force of gravity between objects 1 and 2. (Note, this is identical to the usual expression of gravity, except for the power of r).

Which of the following would be a correct expression of the gravitational potential energy of an object with mass $m$ at a distance $r$ from a star with mass $m_s$?

Treat the energy when the two objects are infinitely far away as being zero.

A

$-G\frac{m_1 m_2}{r^3}$

B

$-G\frac{m_1 m_2}{r^2}$

C

$G\frac{m_1 m_2}{r^2}$

D

$-G\frac{m_1 m_2}{2r^2}$

E

$G\frac{m_1 m_2}{2r^2}$

F

$-G\frac{m_1 m_2}{r}$