A uniform wire of mass m, length L, area of cross-section A and Young's modulus Y hange from the ceiling. Its elongation under its own weight will be

Options

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

Answer

B

Explanation

In case of elongation by its own weight mg will act at centre of gravity of the wire so that length of wire which is stretched will be `((L)/(2))`.
`:. Delta L= ((mg) ((L)/(2)))/(AY) = (mgL)/(2AY)`