Problem 1.140

A small bar \(A\) resting on a smooth horizontal plane is attached by threads to a point \(P\) (Fig. 1.34 ) and, by means of a weightless pulley, to a weight \(\hat{B}\) possessing the same mass as the bar itself. Besides, the bar is also attached to a point \(O\) by means of a light nondeformed spring of length \(l_{0}=50 \mathrm{~cm}\) and stiffness \(x=5 \mathrm{mg} / l_{0}\) where \(m\) is the mass of the bar. The thread \(P A\) having been burned, the bar starts moving. Find its velocity at the moment when it is breaking off the plane.