Question

When a wire is stretched to double its length:

• A. Its radius is halved
• B. Longitudinal strain is unity
• C. Stress is equal to two times Young’s modulus
• D. Young’s modulus is equal to thrice the energy per unit volume

Hint:

For stretching problems: - Volume remains constant. - Use the relation \( r' = \frac{r}{\sqrt{\text{stretch ratio}}} \).

Answer 1

The Correct Option is A

When a wire is stretched, its volume remains constant. Let the initial length be \( L \) and radius \( r \), and after stretching, the new length is \( 2L \).
Since volume is conserved:
\[ \pi r^2 L = \pi r'^2 (2L) \] \[ r'^2 = \frac{r^2}{2} \] \[ r' = \frac{r}{\sqrt{2}} \] Since \( \sqrt{2} \approx 1.414 \), the radius is slightly more than half but approximately close.