Circular Accelerometer

A bead is positioned on a friction-less circular wire with a radius of 1. There is a uniform downward gravitational acceleration \(g\).

The horizontal acceleration of the wire is \(a\, (= 2g)\). Determine the location on the wire at which the bead could be placed, such that it would remain at rest relative to the ring. Give your answer as the horizontal distance from this location to the wire's vertical axis of symmetry.

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