A thick rope of density `rho` and length `L` is hung from a rigid support. The increase in length of the rope due to its own weight is (`Y` is the Young's modulus)

Options

A. `(1)/(4Y)rhoL^2g`
B. `(1)/(2Y)rhoL^2g`
C. `(rhoL^2g)/(Y)`
D. `(rhoLg)/(Y)`

Answer

B

Explanation

As the weight of wire acts at centre of gravity. Only half the length of wire gets extended.
Now. `Y=(F)/(A).(((L)/(2)))/(trianglel)=(Mg((L)/(2)))/(Atrianglel)`
`impliestrianglel=(MgL)/(2AY)impliestrianglel=(ALrhogL)/(2AY)`
`trianglel=(rhoL^2g)/(2Y)`
So the correct choice is (b)