Paragraph A thin uniform rod of length and mass m lies on a frictionless fixed horizontal surface. It is struck with a quick horizontal blow (directed perpendicular to the rod) at a distance x from the center of rod. A dot is painted on the horizontal surface at a distance d from the initial position of the center of the rod. Question For the rod to make one complete revolution by the time the center reaches the dot,

Step-by-step solution

L = dt = x Fdt = x P (because x is essentially constant during the quick blow) since, the rod starts at rest, the final values therefore satisfy L=x P . 1 12 ~m ^2 = xmv v = 12 x ^2 ....(1) Another expression for v is obtained from the given information that rod makes one revolution by the time centre reaches the dot. t =2 and vt = d v = 2 ~d ....(2) from equation 1 and 2: 12 x ^2 = 2 d x = ^2 6 ~d