A uniform chain of mass M and length L is held vertically in such a way that its lower endjust touches the horizontal floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length x has reached the floor.

Given that the mass of chain is M and length is L.


Let us consider a small element of length ‘dx’ at a distance ‘x’.


So, mass of the small element will be



The velocity with which the element will strike the floor is v



Therefore, the momentum transferred to the floor is p




Because the small element comes to rest


So, the force exerted on the floor change in momentum is given by




Becausefor the chain element






Again, the force exerted due to ‘x’ length of the chain on the floor due to its own weight is given by




So, the total force exerted is given by





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