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^(6) kg m^(-3)` and `g = 10 ms^(-2)`)

Options

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

Answer

d

Explanation

As, `Y = (Mg)/(A) xx (L//2)/(Delta L)`
(Length is taken as `(L)/(2)` because weigth acts ias centre of gravity (CG))
Now, `M = A L 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 g L^(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 = 96 xx 10^(-3) m`
= 96 m