Question

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

• A. $Length=50cm,diameter=0.5mm$
• B. $Length=100cm,diameter=1mm$
• C. $Length=200cm,diameter=2mm$
• D. $Length=300cm,diameter=3mm$

Answer 1

Answer: (A)

$Length=50cm,diameter=0.5mm$

Using Hook'e law $Y=\frac{FL}{A\Delta L}$ where $A=\frac{\pi D^2}{4}$

$⟹$ $\Delta L=K\frac{L}{D^2}$ where $K=constant$

For wire A : $\frac{L}{D^2}=\frac{50}{(0.05{)}^2}=20000$

For wire B : $\frac{L}{D^2}=\frac{100}{(0.1{)}^2}=10000$

For wire C : $\frac{L}{D^2}=\frac{200}{(0.2{)}^2}=5000$

For wire D : $\frac{L}{D^2}=\frac{300}{(0.3{)}^2}=3333.33$

Thus wire A has the largest extension.