Q. A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force F its length increases by $l$. Another wire of the same material of length 4 L, radius 4r is pulled by a force 4F. The increase in length will be
A) $\frac{l}{2}$
B) $l$
C) $2l$
D) $4l\ $
Explanation
(b) $Y = \frac{FL}{\pi r^{2}}\ \ or\ l = \frac{FL}{\pi r^{2}Y}\ or\ l\ \propto \frac{Fl}{r^{2}}$
$\frac{l_{1}}{l_{2}} = \ \frac{F\ \times L}{r^{2}}\ \times \ \frac{\left( 4r^{2} \right)}{4F\ \times 4L}$
Or $l_{1} = l_{2} = l$
So, $l$ remain unchanged.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.