A weightless rigid rod with a load at the end is hinged to a point on the wall, so that it can rotation in all directions.

###### Not original.

The rod is kept in the horizontal position with the help of an inextensible thread of length \(l\), fixed at its midpoint. The load receives a momentum in the direction perpendicular to the plane of the figure. Determine the period \(T\), of the small oscillation of the system.

Let this be given by \(2\pi \sqrt{\dfrac{al}{bg} }\), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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