Question

In given figure, a wire is subjected to a gradually increasing force $F$, which causes an extension $l$. The way in which $l$ depends on $F$ is shown by the line $OP.$ The force is then gradually reduced and the relation between $l$ and $F$ in this case is shown by the line $PQ$. Which one of the shaded areas in the graphs below correctly represents the mechanical energy that can be recovered from the wire in this process?

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

If we redraw the graph with the axes interchanged we get,
The curve shows that the extended length is not fully gained back. While coming back, $P2Q$ is the $F$ and I curve, hence area below it shows the mechanical energy recovered.
The mechanical energy spent in extending the wire is the area below O1P , and the energy lost or hystereses is area inside $O-1-P-2-Q-O$.