Gravitational Collapse

Four identical co-planar point masses are arranged in a symmetrical cross formation around the origin, as shown in the diagram. They are initially at rest, with the masses on the vertical axis being twice as far from the origin as those on the horizontal axis. The masses are free to move.

The system collapses under mutual gravitational attraction \((\)there is no ambient \(g\)-field\().\) Let \(x\) be the distance of the masses on the horizontal axis from the origin, and let \(y\) be the distance of the masses on the vertical axis from the origin.

When \(x\) is one tenth of its original value, what is \(\large{\frac{y}{x}}\) (to two decimal places)?

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