Question

A plot of stress vs strain for a copper wire follows a straight line graph. Instead of a copper wire, if a copper rod was considered, then the plot of stress vs strain will show
A) a circle
B) a straight line
C) a straight line with decreasing slope
D) a straight line with intercept equal to the thickness of the rod

Answer 1

Hint:For any stress vs strain graph, we need to find the slope of the graph as slope is going to be a modulus that represents the stiffness or resistance of the material to deform in that particular direction.
\[E=\dfrac{s}{e}\]
E is the slope of the Stress-Strain graph.

Complete step by step solution: The slope of the stress – strain relationship gives the young modulus of the wire and is a feature of the wire's material.
 If it is a tensile test it will be the Young's modulus of elasticity or generally the modulus of elasticity. If it is a shear test it will be the shear modulus or modulus of stiffness. If this is a compression test, it will be Young's modulus again for most materials.
Thus, it will be a constant for any type of arrangement of copper, whether it is a rod or a wire or a plate.
Thus, option B is correct

Additional Information: In mechanics, stress is defined as the force applied per unit area. It is given by formula
$\eqalign{
  & \sigma = \dfrac{F}{A} \cr
  & \sigma \;{\text{is the stress applied}} \cr
  & {\text{F is the force applied}} \cr
  & {\text{A is the area of force application}} \cr} $
Stress is the force applied to a material, divided by the cross-sectional area of ​​the material. Stress is the deformation or displacement of a material that arises from an applied stress. According to the definition of stress, it is defined as the amount of deformation experienced by the body in the direction of the force divided by the initial dimensions of the body. The relation for deformation in terms of the length of a solid is given below.
$\eqalign{
  & \varepsilon = \dfrac{{\delta l}}{L} \cr
  & \varepsilon \;{\text{is the strain due to stress applied}} \cr
  & \delta l\;{\text{is the change in length}} \cr
  & {\text{L is the original length of the material}}{\text{.}} \cr} $
The relation between stress and strain is that they are directly proportional to each other to an elastic limit. Hooke's law explains the relationship between stress and strain. According to Hooke's law, the stretch in a solid is proportional to the applied stress and must be within the elastic limit of that solid.
Notes:The stress – strain diagram provides a graphical measurement of the strength and elasticity of the material. Also, the behavior of the material can be studied with the help of a stress-strain diagram which makes it easier with the application of these materials.
The SI unit of stress is Newton per square meter. Or we can express it in terms of Pascal.
1 pascal = 1 Pa = 1\[N{m^{-2}}\]
While there is no unit for strain. It is a dimensionless quantity. This is because it is the ratio of the change in length to the original length, and is therefore unit less.