A fine uniform chain of mass M and length a is held at rest hanging vertically downwards with its lower end just touching a fixed horizontal table. The chain is then released. Show that, while the chain is falling, the force that the chain exerts on the table is always three times the weight of chain actually lying on the table. [Assume that, before hitting the table, the chain falls freely under gravity.]
∗ When all the chain has landed on the table, the loose end is pulled upwards with the constant force 31Mg. Find the height to which the chain will first rise. [This time, assume that the force exerted on the chain by the table is equal to the weight of chain lying on the table.]