Question

A wire of length $2L$ and radius $r$ is stretched between two supports $A$ and $B$ without any tension. It is then stretched like $AOB$ as shown in the figure below with tension $\frac{CY{r}^2{d}^2}{L^2}$. If $Y$ is Young's modulus of wire, find $C$. (Take $\pi =3.14$ )

Answer 1

Answer: 1.57

$T=\frac{YAl}{L}$
Increase in length of one segment of wire
$l=\left(L+\frac{1}{2}\frac{d^2}{L}\right)-L=\frac{1}{2}\frac{d^2}{L}$
$\therefore T=\frac{Y\pi r^2{d}^2}{2L^2}$
$\Rightarrow C=\frac{\pi }{2}=\frac{3.14}{2}=1.57$