Question

A wire of cross section `A` is stretched horizontally between two clamps located `2lm` 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 1` the strain produced is
A. `(2x^(2))/(l^(2))`
B. `(x^(2))/(l^(2))`
C. `(x^(2))/(2l^(2))`
D. none of these

Answer 1

Correct Answer - C
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))`