It is generally said that the particle is bound into the conservative field when the mechanical energy is negative and zero is the limiting case and the particle will escape the field when the mechanical energy becomes positive. What is the reason behind it?
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From the comments:
By @naturallyInconsistent
For convenience, we chose to put the conventional dividing line for this thing so that zero is the limiting case. i.e. it is a choice, a very natural choice.
By @hft
By convention one chooses the value zero for the potential value at infinity. You can choose that constant value however you like since only the gradient of the potential matters. For example, it is conventional to choose the potential energy of an atomic Coulomb potential as $\frac{Ze^2}{r}$, but you could equally well use $u_0+\frac{Ze^2}{r}$, where $u_0$ is any constant value.