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)/(AY)`
C. `(mgL)/(2AY)`
D. `(2mgL)/(AY)`

Answer

C

Explanation

Since the entire weight `mg` of the wire is concentrated at it at its centre of mass which lies at the geometrical centre
of the wire. So the effective original length of the wire is `(L)/(2)`. According to Hooke's Law
`Y=(stress)/(strai n)`
`Y=((mg)/(A))/((triangleL)/((L)/(2)))impliestriangleL=(mgL)/(2AY)`