A light rod of length l is rigidly attached to a small heavy block at one end and a hook at the other end, as shown in the figure. The system is released from rest while the rod is in a horizontal position. A fixed smooth ring is located at a depth h below the initial position of the hook, and the hook catches into the ring as it reaches there. Determine the minimum value of h required so that the block moves in a co

Step-by-step solution

Let the mass of the heavy block be m . Since the system is released from rest in a horizontal position, it undergoes pure translational motion downwards under gravity. When the hook has fallen a depth h , the block has also fallen a depth h . The velocity of the system just before the hook catches the ring is given by: v = 2gh (directed vertically downwards) When the hook catches the smooth ring, it acts as a fixed pivot. At this instant, the rod is horizontal, and the velocity of the block is perpendicular to the