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Assertion Upto the elastic limit, strain...

Assertion Upto the elastic limit, strain `prop` stress.
Reason Upto elastic limit, material returns to its original shape and size, when external force is removed.

A

If both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If both Assertion and Reason are false.

Text Solution

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The correct Answer is:
To analyze the given assertion and reason, we will break down the concepts of elasticity, stress, strain, and the definitions of the proportional limit and elastic limit. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "Up to the elastic limit, strain is proportional to stress." - According to Hooke's Law, this is true only up to the proportional limit, not the elastic limit. Beyond the proportional limit, the relationship may not hold true. 2. **Understanding the Reason**: - The reason states that "Up to the elastic limit, the material returns to its original shape and size when the external force is removed." - This statement is partially correct. While materials do return to their original shape and size within the elastic limit, the elastic limit is the maximum extent to which a material can be deformed elastically. Beyond this point, some permanent deformation may occur. 3. **Identifying the Proportional Limit and Elastic Limit**: - The proportional limit is the point on the stress-strain curve where stress is directly proportional to strain (Hooke's Law applies). - The elastic limit is the maximum stress that a material can withstand without permanent deformation. Beyond this point, the material may not return to its original shape. 4. **Conclusion**: - Since the assertion incorrectly states that strain is proportional to stress up to the elastic limit (it is only true up to the proportional limit), the assertion is false. - The reason is also misleading because while materials return to their original shape within the elastic limit, the statement implies that this is true up to the elastic limit without acknowledging the proportional limit distinction. 5. **Final Answer**: - Both the assertion and the reason are false. Therefore, the correct conclusion is that both statements are incorrect.
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Knowledge Check

  • Assertion : The elastic spring force arises due to the net attraction or repulsion between the neighbouring atoms of the spring when it is elongated of compressed. Reason : The laws of derived forces such as spring force, friction force are independent of the laws of fundamental forces in nature.

    A
    If both assertion and reason are true and reason is the correct explanation of assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true but reason is false.
    D
    If both assertion and reason are false.

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