Question

Does stress depend on the young's modulus?

Answer 1

Hint: We are asked if stress and young’s modulus is related or dependent on each other. We start by defining stress and young’s modulus. We then give the equations or formula to find the both and see if they are related to each other mathematically. Then we see if the definition gives us an idea about how they are related. This will lead us right to our solution.

Formulas used: The formula used to find the stress of a material is, \[\sigma = \dfrac{R}{A}\]
The formula used to find the young’s modulus of a material is, \[Y = \dfrac{\sigma }{\varepsilon }\]
Where \[R\] is the total resistance force
\[A\] is the area in which the force is acting
\[\varepsilon \] is the strain

Complete answer:
 Let us start by defining both the terms.
Stress: It is a physical quantity that gives us an idea about the motion of particles in a material when a force is applied, that is, stress expresses the forces that neighboring particles of a continuous medium exert on one another. The formula of stress is given as, \[\sigma = \dfrac{R}{A}\]
Young’s modulus: It is a measure of elasticity. The young’s modulus of a material is defined as the ratio between the stress and the strain produced by this stress. The formula to find the young’s modulus is
\[Y = \dfrac{\sigma }{\varepsilon }\]
In conclusion, stress and young people's modulus are dependent on each other.

Note: The young’s modulus is one of the three elastic constants. The others are the bulk modulus and the rigidity modulus. Bulk modulus is considered when the stress caused changes the volume of the body and the rigidity modulus is the ratio of shear stress to shear strain.