A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (figure). A mass m is suspended from the mid-point of the wire. Strain in the wire is

Options

A. `(2x^(2))/(l^(2))`
B. `(x^(2))/(l^(2))`
C. `(x^(2))/(2l^(2))`
D. none of these

Answer

C

Explanation

Here change in length is
`/_\l=(AC+BC)-2l`
`=2(l^(2)+x^(2))^(1/2)-2l`

`2l(1+x^(2)/(l^(2)))^(1//2)`
`=2l(1+1/2(x^(2))/(l^(2)))-2l=(x^(2))/l`
`:.` Strain `=(/_\l)/(2l)=(x^(2))/(2l^(2))`