A thick rope 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 the ceiling of room the increase in its length due to its own weight is .......... `(g = 10 ms ^(-2))`

Options

A. `9.6 xx 10 ^(-5) m`
B. `19.2 xx 10 ^(-7) m`
C. `9.6m`
D. `9.6 xx 10^(-2) m`

Answer

D

Explanation

If the ength of rope is l, the increase in length in rope is only `(l)/(2).`

Now `Y = F/A xx ((l)/(2) )/( Delta L ) = (Wl )/( 2 A Delta l ) [ because F = W` weight]
`therefore Y = (mgl )/( 2 A Delta l ) = (A l rho gl )/( 2 A Delta l ) " "[because m = A l rho ]`
`therefore Y = (rho g l ^(2))/( 2 Delta l )`
`therefore Dl = (rho g l ^(2))/( 2Y) =(1.5 xx10 ^(3) xx 10 xx (8) ^(2))/( 2 xx 5 xx 10 6^(6))`
`therefore Delta l =9.6 xx 10 ^(-2) m`