If material is loaded within the elastic limit then the slope of the stress-strain curve:

CONCEPT:

Stress:

• Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
  • The standard unit of stress is N/m2.

Strain:

• Strain is a measure of the deformation of the material as a result of the force applied.
  • The strain is a unitless quantity.

Hooke's law:

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to the strain produced.

⇒ Stress ∝ Strain

⇒  Stress = E × Strain (Where E = modulus of elasticity)

\( \Rightarrow σ=\frac{F(N)}{A(m^2)}\)    

\( \Rightarrow strain=\frac{dl}{l}\)    

\( \Rightarrow σ=strain\times E\)    

where σ = stress, F = applied force, A = cross-sectional area, dl = change in length, l = initial length and E = young's modulus of elasticity

EXPLANATION:

• Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to the strain produced.

⇒ Stress ∝ Strain

⇒  Stress = E × Strain

\(\Rightarrow E=\frac{stress}{strain}=slope\,of\,stress\,strain\,curve\)     -----(1)

Where E = young's modulus of elasticity

• So by equation 1, we can say that the slope of the stress-strain curve is equal to the young's modulus of elasticity. Therefore, the slope of the stress-strain curve depends on the young's modulus of elasticity. Hence, option 2 is correct.