Copper of fixed volume 'V' is drawn into wire of length 'l'. When this wires is subjected to a constant force 'F', the extension produced in the wire is 'Δl '. which of the following graphs is a straight line?

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Δl versus l²

Δl versus 1/l²

Δl versus l

Δl versus 1/l

answer is A.

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Detailed Solution

Al = V = constant

$∴ A = V / L$
By Hooke's Law,
$\frac{F}{A} = Y \cdot \frac{Δl}{l}$
$\Rightarrow Δl = \frac{FL}{AY} = \frac{{FL}^{2}}{VY}$
$∴ Δl \propto (L^{2})$
$\Rightarrow Δl = C . (L^{2})$
So Δl vs l² is a straight line passing through the origin.

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