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 ${}^{\prime }\Delta l^{\prime }$. Which of the following graph is a straight line?

• A. $\Delta lvs\frac{1}{l}$
• B. $\Delta lvs{l}^2$
• C. $\Delta lvs\frac{1}{l^2}$
• D. $\Delta lvsl$

Answer 1

The correct option is B $\Delta lvs{l}^2$

$V=Al$ (standard result)

$Y=\frac{F/A}{\frac{\Delta l}{l}}$ (standard formula)

$\frac{Y\Delta l}{l}=\frac{F}{A}$

$\Delta l=\frac{Fl}{YA}=\frac{F}{Y}\cdot \frac{ll}{V}$

$\Delta l=\frac{F}{YV}{l}^2$

$\Delta l\propto l^2$