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

Options

A. `1/(4Y)pL^(2)g`
B. `1/(2Y)pL^(2)g`
C. `(pL^(2)g)/Y`
D. `(pLg)/Y`

Answer

B

Explanation

As the weight of wire acts at centre of gravity.
`therefore` Only half the length of wire gets extended.
Now Y`=F/A.((L//2))/(Deltal)rArrDeltal=(ALpgL)/(2AY)`
`thereforeDeltal=(pL^(2)g)/(2Y)`
So the correct choice is (b).