A cylindrical container of dimensions shown in figure has fluid filled completely.

The container is rotated about its axis about angular velocity \(\omega\).

Find the angular velocity \(\omega\), such that \( \dfrac14\) of the base of container is visible.

If the answer is of the form \( \omega = \sqrt{\dfrac {ag}{bR} } \), where \(a,b\) are coprime positive integers, find \(a+b\).

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