Hooke’s law states that *within elastic limit, the elongation produced in a elastic body is directly proportional to the applied tension.* \[\text{i.e. Tension}∝\text{Elongation}\] \[F∝x\] \[F=kx\] where, $k$ is **force constant** or **spring constant**. It is defined as the force applied per unit elongation. Its value depends upon the shape and nature of the material. It may also be defined as the amount of force needed to extend the body by unit length. Its SI unit is $\text{Nm}^{-1}$.

If we consider restoring force (intermolecular force) instead of applied force, then \[F=-kx\] where negative sign indicates that restoring force acts opposite to the elongation.

Now, stress is a measure of the applied deforming force and strain is a measure of the distortion. Therefore, Hooke’s law can be restated in terms of stress and strain, which eliminates the dependency of proportionality constant on shape and size of the body.

We have, \[F=kx\] Dividing both sides by area $(A)$, \[\frac{F}{A}=\frac{kx}{A}\] \[\frac{F}{A}=\frac{kx}{A}\cdot \frac{L}{L}\] \[\frac{F}{A}=\frac{kL}{A}\cdot \frac{x}{L}\] \[\text{stress}=\text{constant}×\text{strain}\] \[\therefore \text{stress}∝\text{strain}\]

Thus, Hooke’s law states that* within elastic limit, stress produced in the body is directly proportional to strain.*

\[\frac{\text{stress}}{\text{strain}}=\text{constant }(E)\] where, the proportionality constant $(E)$ is known as modulus of elasticity. Its value depends upon the nature of the substance, the nature of deformation and temperature.

Since stress is measured in $\text{Nm}^{-2}$ and strain has no unit, the unit of modulus of elasticity is same as that of stress, i.e. $\text{dyne cm}^{-2}$ in CGS system and $\text{Nm}^{-2}$ or $\text{Pa}$ in SI system.

**More on Elasticity**

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