Gravitationally Equivalent Point Particle

There are two objects with the same mass \(M\), situated on the \(x\)-axis.

One is a thin rod with its mass uniformly distributed between \(x = 0\) and \(x = 1\).

The other is a point particle at \(x = 2\).

If we wanted to replace the rod with a point particle of mass \(M\) which would exert the same gravitational force on the point particle at \(x = 2\), what should its \(x\)-coordinate be (to 3 decimal places)?

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