Q. The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?
A) L = 400 cm, r = 0.8 mm
B) L = 300 cm, r = 0.6 mm
C) L = 200 cm, r = 0.4 mm
D) L = 100 cm, r = 0.2 mm
Explanation
(d) Young’s modulus $\ \ Y = \frac{F}{A} \times \frac{L}{l}$
$\ Y = \frac{F}{{\pi r}^{2}} \times \frac{L}{l}$
$Y \propto \frac{L}{r^{2}}$
Option (d) has the largest extension when the same tension is applied.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.