Question

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?

• A. $\Delta l \, \, \, versus \, \, \, \, 1/l$
• B. $\Delta l \, \, \, \, versus \, \, \, \, l^2$
• C. $\Delta l \, \, \, \, \, versus \, \, \, \, \, \, 1/l^2$
• D. $\Delta l \, \, \, \, \, \, \, versus \, \, \, \, \, \, l$

Answer 1

Answer: (B)

$\Delta l \, \, \, \, versus \, \, \, \, l^2$

Answer 2

As V = Al \hspace30mm ...............(i)
where A is the area of cross-section of the wire.
Young's modulus, $Y= \frac{F/A}{ \Delta l / l} = \frac{Fl}{ a \Delta l}$
$\Delta l =\frac{Fl }{YA} = \frac{ Fl^2}{ YV}$ \hspace25mm (Using (i))
$\Delta l \propto l^2$
Hence, the graph between $\Delta l \, \, and \, \, \, l^2$ is a straight
line.