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

Options

A. `96 xx 10^(-3) m`
B. `19.2 xx 10^(-5) m`
C. `9.4 cm`
D. `9.6 m`

Answer

c

Explanation

Due to own weight,
`Delta I = (mgl)/(2AY) = ((IA rho)gl)/(2AY) = (I^(2) rho g)/(2Y) = ((8)^(2) (1.5 xx 10^(3))(9.8))/(2 xx 5 xx 10^(6))`
`= 9.4 xx 10^(-2) m = 9.4 cm`