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Assertion : For small deformations, the ...

Assertion : For small deformations, the stress and strain are proportional to each other.
Reason: A class of solids called elastomers does not obey Hooke's law.

A

Both assertion and reason are true and reason is the correct explanation of assertion.

B

Both assertion and reason are true but reason is not the correct explanation of assertion.

C

Assertion is true but reason is false.

D

Both assertion and reason are false.

Text Solution

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The correct Answer is:
To solve the given question, we need to analyze both the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states: "For small deformations, the stress and strain are proportional to each other." - This statement is true and is derived from Hooke's Law, which states that within the elastic limit of a material, the stress applied to it is directly proportional to the strain produced. Mathematically, this can be expressed as: \[ \sigma = E \cdot \epsilon \] where \(\sigma\) is the stress, \(E\) is the modulus of elasticity, and \(\epsilon\) is the strain. ### Step 2: Analyze the Reason The reason states: "A class of solids called elastomers does not obey Hooke's law." - This statement is also true. Elastomers are materials that exhibit significant elastic deformation when a small amount of stress is applied. Unlike materials that obey Hooke's law, elastomers can experience large strains for relatively small stresses, indicating that they do not maintain a linear relationship between stress and strain. ### Step 3: Determine the Relationship Between Assertion and Reason Now, we need to determine if the reason provided is a correct explanation for the assertion. - Although both the assertion and the reason are true, the reason does not explain why stress and strain are proportional for small deformations. Instead, it highlights an exception (elastomers) to the general rule (Hooke's law). Therefore, the reason does not serve as a correct explanation for the assertion. ### Conclusion Based on the analysis: - The assertion is true. - The reason is true but does not explain the assertion. - Thus, the correct option is: **Both assertion and reason are true, but reason is not the correct explanation of assertion.** ### Final Answer **Option B: Both assertion and reason are true, but reason is not the correct explanation of assertion.** ---
To solve the given question, we need to analyze both the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states: "For small deformations, the stress and strain are proportional to each other." - This statement is true and is derived from Hooke's Law, which states that within the elastic limit of a material, the stress applied to it is directly proportional to the strain produced. Mathematically, this can be expressed as: \[ \sigma = E \cdot \epsilon ...
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