Question

A chain of mass 'm' and length 'l' is kept in three positions as shown below. Assuming h = 0 on the ground find potential energy of the chain in all three cases.

Answer 1

For finding potential energy of chain we will have to see its centre of mass height h from the ground.
In figure (a): $h_c=0\Rightarrow Potentialenergy,U=0$
In figure (b): $h_c=h\Rightarrow Potentialenergy,U=mgh$
In figure (a): $h_c=\frac{1}{2}\Rightarrow Potentialenergy,U=mg\frac{1}{2}$
Yes, we have to consider the height of center of mass from the reference line to find the gravitational potential energy.