A chain of length L and mass m is held vertically so that the bottom link just touches the floor. It is then dropped. 

(a) Show that the acceleration of the top end of the chain is g. 

(b) If the chain is moving downward with speed v at time t, and speed v + ∆v at time t + ∆v, find an expression for the change in momentum of the chain during the interval ∆t. 

(c) Find the force exerted on the chain by the floor.