**Young’s modulus**

** 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/πr_{2}l

[A = area of cross-section of the wire = πr^{2}]

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 10^{11} Nm^{-2} means that within elastic limit it force of 2 x 10^{11} N is applied along the length of a steel wire of 1 mm^{2} 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^{-1}T^{-2}]

Unit of Y: Newton/metre^{2} = [Nm^{-2}]

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