A rigid uniform rod of mass $M$ and length $L$ is resting on a smooth horizontal table. It is pivoted at its centre. Two marbles each of mass $\frac{M}{6}$ moving with uniform speed $L \mathrm{m} {\mathrm{s}}^{-1}$ in the plane of the table collide with the two ends of the rod simultaneously as shown in the figure. The marbles stuck to the rod and continue to move with the rod. Time taken by the rod to rotate through an angle $\frac{\pi }{2}$ radian is (in seconds)