Gravitationally Equivalent Point Mass

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

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

What should its approximate xx-coordinate be?


Inspired by Steven Chase
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