A rubber rope of length 8 m is hung from the ceiling of a room. What is the increases in length of the rope due to its own weight? (Given, Young's modulus of elasticity of rubber `= 5 xx 10^(6) Nm^(-2)` and density of rubber `= 1.5 xx 10^(3) kg m^(-3)` and `g = 10 ms^(-2)`)

Options

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

Answer

D

Explanation

`Y = (Mg)/(A) xx (L//2)/(Delta L)`
(Length is taken as `(L)/(2)` because weight acts at CG)
Now, M= `AL rho`
(For the purpose of calculation of mass, the whole of geometrical length L is to be considered).
`:. Y= (AL rho gL)/(2A Delta L)`
or `Delta L= (rho gL^(2))/(2Y) = (1.5 xx 10^(3) xx 10 xx 8 xx 8)/(2 xx 5 xx 10^(6)) = 9.6 xx 10^(-2) m`
`= 9.6 xx 10^(-2) xx 10^(3) mm = 96mm`