Young's Modulus (Y):

It is defined as the ratio of the longitudinal stress to the longitudinal strain for the material of the body. To write an expression for the Young's modulus, let a wire of length l and area of cross-section A be stretched by a longitudinal force F causing a change Δ l in the length of the wire. Then we can write:

Longitudinal stress = F / A; and

Longitudinal strain = Δ l / l

Therefore, the Young's modulus is written as:

Y =   (F/A)/( Δ l/l)  = Fl/A Δ l

If r is the radius of the wire suspended vertically with a rigid support and M is the mass attached to its free end, we can write:

A =π r ²   and F = M g

Substituting for A and F in Eq. (1.18), we get:

∴          Y = M g l /π r ² Δ l

The units of Young's modulus are Pascal (Pa) or Nm^{- 2} in the SI system.