A wire of cross section `A` is stretched horizontally between two clamps located `2l m` apart. A weight `W kg` is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance `x lt l`, the strain produced 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
`trianglel=[AC+BC]-2l`
`=2(l+x^2)^((1)/(2))-2l`
`=2l(1+(x^2)/(l^2))^((1)/(2))-2l=2l(1+(1)/(2)(x^2)/(l^2))-2l=(x^2)/(l)`
Strain`=(trianglel)/(2l)=(x^2)/(2l^2)`
correct choice is (c ).