A rubber cord of length L is suspended vertically. Density of rubber is D and Young’s modulus is Y. If the cord extends by a length l under its own weight then

Question

A rubber cord of length L is suspended vertically. Density of rubber is D and Young’s modulus is Y. If the cord extends by a length l under its own weight then (A) l=(L2 D g/Y) (B) l=(L2 D g/2 Y) (C) l=(L2 D g/4 Y) (D) l=(L2 D g/8 Y)

Tardigrade Admin · Accepted Answer

Stress =(F/A)=(M g/A) =(A × L × ρ × g/A)=L ρ g(ρ=D) Stress =LDg Strain =(Δ L/L)=(l/L / 2)=(2l/L) Y=(LDg/2l) × L ⇒ l=(L2 D g/2 Y)

Q. A rubber cord of length $L$ is suspended vertically. Density of rubber is $D$ and Young’s modulus is $Y$ . If the cord extends by a length $l$ under its own weight then

$l = \frac{L ^{2} D g}{Y}$

$l = \frac{L ^{2} D g}{2 Y}$

$l = \frac{L ^{2} D g}{4 Y}$

$l = \frac{L ^{2} D g}{8 Y}$

Stress $= \frac{F}{A} = \frac{M g}{A}$
$= \frac{A \times L \times ρ \times g}{A} = L ρ g (ρ = D)$
Stress $= L D g$
Strain $= \frac{Δ L}{L} = \frac{l}{L /2} = \frac{2 l}{L}$
$Y = \frac{L D g}{2 l} \times L$
$\Rightarrow l = \frac{L ^{2} D g}{2 Y}$

Q. A rubber cord of length L is suspended vertically. Density of rubber is D and Young’s modulus is Y. If the cord extends by a length l under its own weight then

l=YL2Dg​

l=2YL2Dg​

l=4YL2Dg​

l=8YL2Dg​