Question

What will be the loss in potential energy of chain (mass $m$) when half of its length is grounded.

Answer 1

Chain is uniform & it is like a straight line. Now the com of chain will be at the mid point of the vertical length.

So initially com is at $\frac{L}{2}\therefore P.E=\frac{mgL}{2}$

Now, the $\frac{mass}{length}=\frac{m}{L}$

When half of the length of the chain is grounded the $P.E.$of the grounded part $=0$

Mass of the remaining part $=\frac{m}{2}$

Vertical length now $=\frac{l}{2}$

$\therefore$ Com is at mid point of this vertical length $=\frac{l}{4}$

$\therefore P.E.$ now $=\frac{mgl}{4}$

$\Delta P.E.=\frac{mgl}{2}-\frac{mgl}{4}=\frac{mgl}{4}$