A thick rubber rope of density ρ 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

Question

A thick rubber rope of density ρ 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) (1/2) ρ g L2 Y (B) (ρ g L2/2 Y) (C) (ρ g L/Y) (D) (ρ g L/6 Y)

Tardigrade Admin · Accepted Answer

L eq =(L/2) Y=(F ⋅ Le q/A x) or x=(F ⋅(L / 2)/A ⋅ Y)=((ρ L A g) L/A ⋅ Y ⋅ 2) ⇒ x=(ρ ⋅ g L2/2 Y)

Q. A thick rubber rope of density $ρ$ 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

$\frac{1}{2} ρ g L^{2} Y$

$\frac{ρ g L ^{2}}{2 Y}$

$\frac{ρ gL}{Y}$

$\frac{ρ gL}{6 Y}$

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

Q. A thick rubber rope of density ρ 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

21​ρgL2Y

2YρgL2​

YρgL​

6YρgL​