A mild steel wire of length `1.0m` and cross sectional area `2L` is strethched, within its elastic limit horizontally between two pillars(figure). A mass of `m` is suspended form the midpont 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

Refer Fig. 7(EP).5, increase in length `=BO+OC-BC`
or `Delta L=2 BO- 2L =2(L^(2)+x^(2))^(1//2)- 2L`
or `Delta =2L[1+(x^(2))/(L^(2))]^(1//2) - 2L=(x^(2))/(L)`
`:.` Strain `=(Delta L)/(2L)=(x^(2)//L)/(2L)= (x^(2))/(2L^(2))`