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. $l=\frac{L^{2} D g}{Y}$
• B. $l=\frac{L^{2} D g}{2 Y}$
• C. $l=\frac{L^{2} D g}{4 Y}$
• D. $l=\frac{L^{2} D g}{8 Y}$

Answer 1

Answer: (B)

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