The Hooke's law is valid for
A) only proportional region of the stress strain curve B) entire stress strain curve C) entire elastic region of the stress strain curve D) elastic as well as plastic region of the stress strain curve
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Hooke’s Law
Hooke’s Law states that for small deformities, the stress and strain are proportional to each other. Thus,
Stress
∝
∝ Strain
Or, Stress = k × Strain … where k is the constant of proportionality and is the Modulus of Elasticity. It is important to note that Hooke’s Law is valid for most materials.
Stress-Strain Curve
To determine the relation between the stress and strain for a given material, let’s conduct an experiment. Take a test cylinder or wire and stretch it by an applied force. Record the fraction change in length (strain) and the applied force needed to cause the strain. Increase the applied force gradually, in steps, and record the readings.
Now, plot a graph between the stress (which is equal in magnitude to the applied force per unit area) and the strain produced. The graph for a typical metal looks as follows:
Hooke's Law
The stress-strain curves can vary with the material in question. With the help of such curves, we can understand how the material deforms with increasing loads.
Analysis of the Curve
In Fig. 2, we can see that in the region between O and A, the curve is linear. Hence, Hooke’s Law obeys in this region. In the region from A to B, the stress and strain are not proportional. However, if we remove the load, the body returns to its original dimension.
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Hooke’s Law states that for small deformities, the stress and strain are proportional to each other. Thus,
Stress
∝
∝ Strain
Or, Stress = k × Strain … where k is the constant of proportionality and is the Modulus of Elasticity. It is important to note that Hooke’s Law is valid for most materials.
Stress-Strain Curve
To determine the relation between the stress and strain for a given material, let’s conduct an experiment. Take a test cylinder or wire and stretch it by an applied force. Record the fraction change in length (strain) and the applied force needed to cause the strain. Increase the applied force gradually, in steps, and record the readings.
Now, plot a graph between the stress (which is equal in magnitude to the applied force per unit area) and the strain produced. The graph for a typical metal looks as follows:
Hooke's Law
The stress-strain curves can vary with the material in question. With the help of such curves, we can understand how the material deforms with increasing loads.
Analysis of the Curve
In Fig. 2, we can see that in the region between O and A, the curve is linear. Hence, Hooke’s Law obeys in this region. In the region from A to B, the stress and strain are not proportional. However, if we remove the load, the body returns to its original dimension.
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Hooke's law is valid for the only proportional region of the stress-strain curve. Option(A) is the correct answer.
- According to Hooke's Law, stress and strain are proportional to one another for small deformities.
- The stress-strain curves can change depending on the material. These curves help us understand how the material changes shape as the force increases.
- When the stress-strain curve gradient is linear, this means that as the strain on the body increases at a constant rate, so does the amount of stress.
- The body will back to its former measurements if the applied force is released while it is in the proportionality region.
- Hence, Hooke's law is only applied to the proportionality region of the stress-strain curve.
For more information on Hooke's law and stress-strain curve, refer to the following answers:
https://brainly.in/question/631059
https://brainly.in/question/3910872
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