Gravitational potential from thin rod

Classical Mechanics Level 4

A thin uniform rod of length $L$ and mass $M$ is placed along the $x$ -axis. One end of the rod is placed at the origin and the other end at the point $(L,0).$ Find the gravitational potential at the point $P( a, 0 )$ with $a > L.$

We take the gravitational potential to be zero at $x = \text{infinity}.$

U = \frac{GM}{L}\ln{\frac{a+L}{a}}

U = \frac{GM}{L}\ln{\frac{a-L}{a}}

U = \frac{GM}{L}\ln{\frac{a-L}{a+L}}

U = \frac{GM}{L}\ln{\frac{a}{a-L}}

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Gravitational potential from thin rod

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