A cord of mass m length L, area of cross section A and Young's modulus y is hanging from a ceiling with the help of a rigid support. The elogation developed in the wire due to its own weight is

Options

A. zero
B. `(mgL)/(2AY)`
C. `(mgL)/(AY)`
D. `(2mgL)/(AY)`

Answer

B

Explanation

(b) Tension at distance x from the bottom
`T((mg)/(L))x`
Now, `" " dl=(T.dx)/(AY)`
`:.` The elongation of the wire
`Deltal=int_(0)^(L)dl=(mgL)/(2AY)`