Question

The extension produced in a wire by the application of load is 5 mm. The extension in a wire of the same material and length but half the radius, by the same load is:

• A. 20 mm
• B. 30 mm
• C. 40 mm
• D. 50 mm

Answer 1

Answer: (A)

$Y=\frac{F \times L}{A \times \Delta L}$
$\Rightarrow \Delta L \propto \frac{1}{ r ^{2}}$
$\therefore \frac{\Delta L_{1}}{\Delta L_{2}}=\left(\frac{r_{2}}{r_{1}}\right)^{2}$
$\Rightarrow \Delta L_{2}=\Delta L_{1} \times\left(\frac{r_{1}}{r_{2}}\right)^{2}$
$=5 \times 4=20\, mm$