A flexible but inextensible chain of length `l` is placed on a smooth table with an initial length `1 = nl` hanging down the table. Calcultae the velocity with which the chain will leave the table if released from rest. Consider two cases : (i) the hanging part does not touch the ground which is at a large distance, (ii) the lower end of the hanging part initially just touches the ground. Also calculate the time in which the chain leaves the table in the first case
[Hint : Taking the table as the datum and `m` as the mass per unit length of the chain, apply the principle of conservation of energy].

Answer

(i) `v=sqrt(gl(1-n^(2)))t,=sqrt((l)/(g)ln)((1+sqrt(1-n^(2)))/(n))` (ii) `v=sqrt(2nlg l n(1)/(n))`