Q.
A wire of length $2L$ and radius $r$ is stretched between $A$ and $B$ without the application of any tension. If $Y$ is the Young’s modulus of the wire and it is stretched like $ACB$, then the tension in the wire will be
A) $\frac{\pi r^{2}Yd^{3}}{2L^{2}}$
B) $\frac{\pi r^{2}Yd^{2}}{2L^{2}}$
C) $\frac{\pi r^{2}Y.2L^{2}}{d^{2}}$
D) $\frac{\pi r^{2}Y.2L}{d}$
Explanation
(b) $T = \frac{YAl}{L}$
Increase in length of one segment of wire
$l = \left( L + \frac{1}{2}\frac{d^{2}}{L} \right) - L = \frac{1}{2}\frac{d^{2}}{L}$
So, $T = \frac{Y\pi r^{2}.d^{2}}{2L^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.