Question

A steel wire of length 'l' and radius of cross–section ‘r’ is stretched horizontally between two rigid supports attached at its ends. A load Mg suspended from its midpoint produces a depression of x well within elastic limit of the material of the wire. The Young’s modulus of the material is

(1) \(\frac{Mgl^2}{8\pi r^2x^2}\)

(2) \(\frac{Mgl^4}{8\pi r^2 x^3}\)

(3) \(\frac{Mgl^3}{8\pi r^2 x^3}\)

(4) \(\frac{Mgl}{8\pi r x^2}\)

Answer 1

  (3) \(\frac{Mgl^3}{8\pi r^2 x^3}\)

In Fig, AB is wire of length l . M is mass suspended from mid point C. In equilibrium, point C moves to position D as shown in Fig. Now

The Increased length of wire = ADB = 2DB