1. Tardigrade
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  4. 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 O P . The force is then gradually reduced and the relation between l and F in this case is shown by the line P Q. 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?

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Q. 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 $O P .$ The force is then gradually reduced and the relation between $l$ and $F$ in this case is shown by the line $P Q$. 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?Physics Question Image

Mechanical Properties of Solids

Solution:

image
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 $O-1 -P -2-Q -O$.