Q. The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum ?
A) Length 100 cm, Diameter 1 mm
B) Length 200 cm, Diameter 2 mm
C) Length 300 cm, Diameter 3 mm
D) Length 50 cm, Diameter 0.5 mm
Explanation
(d) $Y = \frac{F}{A}\ \ \ \ \frac{L}{l}\ \Rightarrow l \propto \frac{L}{A}\ \propto \frac{L}{\pi d^{2}}$
$\therefore\ l \propto \frac{L}{d^{2}}$
The ratio of $\frac{L}{d^{2}}\ $is maximum for case (d).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.