According to Hook’s law stress is proportional to
A. Pressure
B. Strain
C. Elasticity
D. Ductility
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Explanation:
Stress: Force (F) applied per unit area (A) is called stress.
\(σ = {F \over A}\)
Unit of stress: N\m2.
Strain: Measure of deformation (Δl) experienced by the body in the direction of force applied, divided by initial dimensions (l) of the body is called strain.
\(ϵ ={ ∆l \over l}\)
Hooke’s law:
It States that under direct loading, within proportionality limit, stress is directly proportional to strain. Hooke's law ibecause helps us understand how a stretchy object will behave when it is stretched or compacted.
Stress ∝ Strain
σ = E × ∈
where σ is stress, ∈ is the strain, E is a Constant of proportionality and known as Young’s modulus of elasticity.
Young’s modulus of elasticity
- The slope of the stress-strain curve is called the modulus of elasticity (E).
- The modulus of elasticity (E) is the constant of proportionality which is defined as the intensity of stress that causes unit strain.
- The modulus of elasticity (E) has the unit the same as that of stress.
Hooke’s law is valid up to the limit proportionality.
- For mild steel proportionally limit and elastic limit are almost equal.
- For other metals, the elastic limit may be higher than the proportionality limit. e.g Rubber.
Stress-Strain Curve:
- The stress-strain curve for a material gives the relationship between change in stress and change in strain.
- Experimentally, It is obtained by gradually applying a load to the system.
- The ratio of stress and strain gives Young's modulus of elasticity.
Limit of proportionality is the stress at which the stress-strain curve ceases to be a straight line. It is the stress at which extension ceases to be proportional to strain. The proportional limit is important because all subsequent theory involving the behavior of elastic bodies is based on the stress-strain proportionality.
Elastic limit is is that point in the stress-strain curve up to which the material remains elastic, i.e. the material regains its shape after the removal of the load.
