A rubber rope of length `8 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 xx 10^(6) N//m^(2)` and density of rubber `=1.5xx10^(3)kg//m^(3)`. Take `g=10ms^(-2))`

Explanation

Given length `= 8m`, Density `rho = 1.5xx10^(3) kg//m^(3)`
Young's modulus,
`Y = 5xx10^(6) N//m^(2), g = 10m//s^(2)`
The increases in its length due to its own weight
`e = (l^(2) rho g)/(2Y) = (8^(2)xx1.5xx10^(3)xx10)/(2xx5xx10^(6)) = 9.6xx10^(-2)m`