Within elastic limit ratio of longitudinal stress and longitudinal strain is a constant. This constant is called Young’s modulus of the material of the body. It is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. It is denoted by Y.
Young’s modulus, Y = longitudinal stress / longitudinal strain
Explanation: Hanging from a rigid support one end of a wire of initial length L and radius r and hanging a load at the other end i.e., by applying force F = mg, if the length of the wire increases by l, then,
Longitudinal stress of the wire = F/A and
Longitudinal strain = l/L
So, Young’s modulus, Y = longitudinal stress / longitudinal strain
then, Y = mgL/πr2l
[A = area of cross-section of the wire = πr2]
If in equation Y = FL/Al, A = l unit and l = L; then Y = F.
So, for a wire of unit cross-sectional area if the increase in length is equal to the initial length for the force applied along the length of the wire, then that is called the Young’s modulus.
Young’s modulus of steel = 2 x 1011 Nm-2 means that within elastic limit it force of 2 x 1011 N is applied along the length of a steel wire of 1 mm2 cross-sectional area, then the increase of length will be equal to the original length.
Dimension of Young’s modulus: [Young’s modulus] = [stress/strain]
or, [Y] = [ML-1T-2]
Unit of Y: Newton/metre2 = [Nm-2]