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))`

Options

A. `1.5mm`
B. `6mm`
C. `24mm`
D. `96mm`

Answer

D

Explanation

`Y=(Mg)/(A)xx((L)/(2))/(triangleL)`
(length is taken as `(L)/(2)` because weight acts at C.G.)
Now, `M=ALrho`
[for the purpose of calculating mass, the whole of geometrical length L is to be considered.]
`Y=(ALrhogL)/(2AtriangleL)`
or `triangleL=(rhogL^2)/(2Y)=(1.5xx10^3xx10xx8xx8)/(2xx5xx10^6)m`
`=9.6xx10^-2m=9.6xx10^-2xx10^3mm`
`=96mm`