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

Options

A. `(x^(2))/(2L^(2))`
B. `(x)/(L)`
C. `(x^(2))/(L)`
D. `(x^(2))/(2L)`

Answer

a

Explanation

Increase in length

`DeltaL=BO+OC-(BC)`
`=2BO-2BD`
`rArrDeltaL=2BO-2L`
`=2[L^(2)+x^(2)]^((1)/(2))-2L`
or `DeltaL=2L[1+(x^(2))/(L^(2))]^((1)/(2))-2L[because "using Bionomial theorem"]`
`rArrDeltaL=2L[1+(1)/(2)(x^(2))/(L^(2))-1]`
`=(x^(2))/(L) " " [becausexltltL]`
`therefore` Strain `=(DeltaL)/(2L)`
`=((x^(2))/(L))/(2L)=(x^(2))/(2L^(2))`