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  4. A wire of length 2 L and radius r is stretched between two supports A and B without any tension. It is then stretched like A O B as shown in the figure below with tension (C Y r2 d2/L2). If Y is Young's modulus of wire, find C. (Take π=3.14 )

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

Mechanical Properties of Solids

Solution:

$T =\frac{ YA l}{ L }$
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}}{2 L^{2}} $
$ \Rightarrow C=\frac{\pi}{2}=\frac{3.14}{2}=1.57$