A wire of leng:h L has a linear mass density `mu` and area of cross-section A and the Youngs modulus Y is susperded vertically from a rigid support. The extension produced 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)`