Q. A 100 N force stretches the length of a hanging wire by 0.5 mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5 mm is
A) 100 N
B) 400 N
C) 1200 N
D) 1600 N
Explanation
(d) $Y = \ \frac{F\ \times 4\ \times 1}{\pi D^{2}\ \mathrm{\Delta}l}$
In the given problem, $F\ \propto D^{2}.\ $Since, D is increased by a factor of, 4, therefore, F is increased by a factor of 16.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.