# Gravitationally Equivalent Point Mass

There are two objects, a thin rod of mass $$M$$ in the interval $$[0,1]$$ on the $$x$$-axis, and a point mass at $$x=2$$ of the same mass $$M$$, as shown above.

Suppose we wanted to replace the rod with a particle of mass $$M$$, which would exert the same gravitational force on the point particle at $$x = 2$$.

What should its approximate $$x$$-coordinate be?

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