A wire of cross-section A is stretched horizontally between two clamps located 21 metre apart. A weight W kg is suspended from the mid point of the wire. If the mid point sags vertically through a distance x < 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
`Deltal=[AC+BC]-2l`
`=2(l^(2)+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`
`therefore` strain`=(Deltal)/(2l)=(x^(2))/(2l^(2))`.
Correct choice is (c).