Question

A thick rubber rope of density $\rho$ and length $L$ is suspended from a rigid support. If $Y$ is the Young's modulus of elasticity of the material of the rope, then the increase in length of the rope due to its own weight is

• A. $\frac{1}{2} \rho g L^{2} Y$
• B. $\frac{\rho g L^{2}}{2 Y}$
• C. $\frac{\rho g L}{Y}$
• D. $\frac{\rho g L}{6 Y}$

Answer 1

Answer: (B)

$L_{ eq }=\frac{L}{2}$
$Y=\frac{F \cdot L_{e q}}{A x}$
or $x=\frac{F \cdot(L / 2)}{A \cdot Y}=\frac{(\rho L A g) L}{A \cdot Y \cdot 2}$
$\Rightarrow x=\frac{\rho \cdot g L^{2}}{2 Y}$