A chain hanging from a string just touches the surface of the weighing machine. The string is burnt, and the chain falls on the weighing machine. What would be the weight registered on the weighing machine?
I came across certain standard solutions that claimed that the weight displayed by the weighing machine would be $3mgx/l$ when $x$ lies on the table provided $0<x<l$. However the solutions seemed to assume that the tension in the part of the chain that is falling down is $0$ without any justification, and I couldn't come up with a satisfactory explanation.
Could anybody explain, based on what principles do we state that the tension in the string should be 0?
Best Answer
I see that you already have the solution with you. So, I will try to help you with the tension in the chain zero part. The tension here will be zero even if the chain is acceelerating because the acceleration is caused by the gravitational force which is pulling it down and this force is acting on every single atom and molecule of the chain. In other words, at any point of time, the force acting upon any part of the chain with respect any other part of the chain is zero. Hence, there won't be any tension in the chain.