A thin rigid rod of length \(l\) is placed perfectly vertical on a smooth ground. A slight disturbance on the upper end of rod causes lower end of rod to slip along the ground and rod starts falling down. Velocity of centre of mass of rod when the rod is making an angle of \( 30 ^{ \circ }\) with the ground is given by

\[ =\sqrt { \frac { a }{ b } } \sqrt { gl } ,\] where a,b are co-prime integers. Find \( a + b \).

\(g=\)Acceleration due to gravity.

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