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. `x^(2) // I^(2)`
B. `2x^(2) // I^(2)`
C. `x^(2) // 2I^(2)`
D. `x// 2I`

Answer

c

Explanation

From figure the increase in length,
`Delta I = (PR + RQ) - PQ = 2PR - PQ`

`= 2 (I^(2) + x^(2))^(1//2) - 2I = 2I (1 + x^(2))^(1//2) -2I = 2I [1 + (1)/(2). X^(2)] - 2I`
`= x^(2) // I` (by binomial theorem)
`:.` strain `= Delta I // 2I = x^(2) // 2I^(2)`