Newton's Law of Gravitation States That Two Bodies with Masses $m _ { 1 }$

Multiple Choice

Newton's Law of Gravitation states that two bodies with masses $m _ { 1 }$ and $m _ { 2 }$ attract each other with a force
$$F = G \frac { m _ { 1 } m _ { 2 } } { r ^ { 2 } }$$ where $r$ is the distance between the bodies and $G$ is the gravitation constant. If one of bodies is fixed, find the work needed to move the other from $r = l$ to $r = g$ .

A)
$W = G m _ { 1 } m _ { 2 } \left( \frac { 1 } { l ^ { 2 } } - \frac { 1 } { g ^ { 2 } } \right)$
B)
$W = G m _ { 1 } m _ { 2 } \left( \frac { 1 } { l } - \frac { 1 } { g } \right)$
C)
$W = G m _ { 1 } m _ { 2 } \left( \frac { 1 } { g ^ { 2 } } - \frac { 1 } { l ^ { 2 } } \right)$
D)
$W = G m _ { 1 } m _ { 2 } \left( \frac { 1 } { g } - \frac { 1 } { l } \right)$
E)
$W = G m _ { 1 } m _ { 2 } \left( \frac { 1 } { l ^ { 2 } } + \frac { 1 } { g ^ { 2 } } \right)$