Question

Copper of fixed volume 'v; is drawn into wire of length 'l. When this wore 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. $\Delta lversus\frac{1}{l}$
• B. $\Delta lversus{l}^2$
• C. $\Delta lversus\frac{1}{l^2}$
• D. $\Delta lversusl$

Answer 1

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

youngs modulus$Y=\frac{stress}{strain}=\frac{\frac{F}{A}}{\frac{△l}{l}}=\frac{Fl}{△lA}$

given F is constant and Y is constant

since V=Al is constant,$A\alpha \frac{1}{l}$

$△l\alpha \frac{A}{l}\alpha l^2$

$△l\alpha l^2$

so the graph between $△l$ and$l^2$is a straight line