# Working with elastic string

Two equal particles are connected by an elastic string which is just taut on a smooth table, the string being such that the weight of either particle would produce in it an extension $$a$$. If one of the particle is projected with velocity $$u$$ directly away from the other, the distance each particle would have travelled when the string first return to is natural length can be represented as

$2\pi u \sqrt{\dfrac{a}{\alpha g}}$

Where g is acceleration due to gravity, find the value of $$\alpha$$.

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