Rankers Physics

Solids: Practice Problem & Solution

Copper of fixed volume $V$ is drawn into wire of length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line? (2014)
$\Delta l \text{ versus } 1/l$
$\Delta l \text{ versus } l^2$
$\Delta l \text{ versus } 1/l^2$
$\Delta l \text{ versus } l$

Solution Explained:

To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:

Extension $\Delta l = \frac{Fl}{AY}$. Since volume $V = Al$, we have $A = V/l$. Substituting this, $$\Delta l = \frac{Fl}{(V/l)Y} = \frac{Fl^2}{VY}$$. Thus, $\Delta l \propto l^2$, meaning the graph of $\Delta l$ versus $l^2$ is a straight line.

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