A thick rope of rubber of density `1.5 kg//m^(3)` and `Y = 5 xx 10^(6) Nm^(-2)` 8 metres in length when hung vertically will increase in length by : `(g = 10 ms^(-2))`

Options

A. `9.6 xx 10^(-5)` m
B. 9.6 m
C. `19.2xx10^(-3)m`
D. `19.2xx10^(-5)m`

Answer

A

Explanation

As the weight of wire is at centre of gravity.
`therefore` Only half the length ofrope gets extended.
`Y=F/A.((L//2))/(Deltal)`
`thereforeDeltal=(Mg)/(AY).L/2=(ALpg.h)/(2Ay)=(L^(2)pg)/(2Y)`
`=(64xx1.5xx10)/(2xx5xx10^(6))=9.6xx10^(-5)m`
So, the correct choice is (a).