If the figure above, 2 thin identical hoop's of radius \(r=1 \text{ m}\) and mass \(M=9\text{ kg}\) are placed on a rough floor. They are connected by a small ring of mass \(m=4\text{ kg}\) at \(A\). Now, the hoops move apart. What is the acceleration of the ring at initial instant?

**Details and Assumptions**:

\(g=10 \text{ ms}^{-1}\).

\(\angle ABC=\angle ACB={ \left( \dfrac { \pi }{ 4 } \right) }^{ c }\).

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