If in the above question the Young's modulus of the material is Y, the value of extension x is:

Options

A. `((Wl)/(YA))^(1//3)`
B. `((YA)/(Wl))^(1//3)`
C. `(l)/(l)((WA)/(Y))^(1//3)`
D. `l((W)/(YA))^(1//3)`

Answer

D

Explanation

`2T sin theta = W` (for small angles `sin theta = tan theta`)
`2T tan theta = W, tan theta = (x)/(sqrt(x^(2) + l^(2))) = (x)/(l)`
`2T (x)/(l) = W, T = (Wl)/(2x), "Stress" = (T)/(A) = (Wl)/(2xA)`
`Y = ("Stress")/("Strain") = (Wl)/(2Ax) xx (2l^(2))/(x^(2)), Y = (Wl^(2))/(Ax^(3)) orx = ((W)/(AY))^(1//3) xx l`