Question 7: Explain Hook’s law and modulus of elasticity.

### Definition of Hook’s law

Within the elastic limit of a material, the stress applied to the material is directly proportional to the strain in the material.

Hook’s law is graphically shown below.

Elastic limit

When a material is stressed (i-e, applied force to it), it will return to its original dimensions when the stress is removed. However, if the stress is gradually increased, a limit reaches when the material would be permanently deformed and will never come back to its original position.

Elastic limit is the maximum stress that can be applied to a material without causing permanent deformation in it. The graph is a straight line passing through the origin. Mathematically,

Stress ∝ Strain ⇒ (stress/strain) = constant

### Modulus of Elasticity

The constant is known as modulus of elasticity. Its unit is newton per meter squared. (Remember strain is a ratio and has no units, therefore, the units of modulus of elasticity and stress are same). Similarly, you can see from the above graph that the gradient of the graph (ΔF/Δl) also gives this constant.