Determine the force $F$ required to give the open link chain a constant velocity $v=\frac{dy}{dt}.$ The chain has a total length $l$. and make per unit length $\lambda$.Neglect the mass and any friction in the pulley.

 If v has to be constant, net pulling force on the chain should be zero. This is possible only when Thrust force + Weight of left side of the chain 

$=Pull F+Weight of right side of the chain$

$$\begin{gathered} Therefore ,\lambda v^2+\lambda hg=F+\left(\lambda y\right)g \\ (\because F_1=v\lambda \frac{dy}{dt}=\lambda v^2\backslash \mathrm{right}) \end{gathered}$$

$or F=\lambda v^2+\lambda g(h-y)$