Question

A rubber rope of length $7\text{m}$ is hung from the ceiling of a room. What is the increase in length of the rope due to its own weight? (Given: Young's modulus of elasticity of rubber = $5\times {10}^6{\text{N m}}^{-2}$ and density of rubber = $1.5\times {10}^3\frac{\text{kg}}{{\text{m}}^3}$ and $g=10\frac{\text{m}}{{\text{s}}^2}$)

• A. $96\text{mm}$
• B. $73.5\text{mm}$
• C. $46\text{mm}$
• D. $92\text{mm}$

Answer 1

The correct option is B $73.5\text{mm}$

The streching of a rod due to its own weight is given by
$\Delta l=\frac{Mgl}{2AY}$---------(1)
We know $M=\rho Al$-------(2)
Putting equation (2) in equation (1) we get,
$\Delta l=\frac{\rho g{l}^2}{2Y}$
Putting the given values,
$\Delta l=\frac{1.5\times {10}^3\times 10\times 7\times 7}{2\times 5\times {10}^6}$
$\Delta l=73.5\times {10}^{-3}\text{m}=73.5\text{mm}$