Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason R : On heating, the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below :

Both A and B are true but R is NOT the correct explanation of A

Both A and R are true and R is the correct explanation of A

Heat and Thermodynamics PYQ — JEE Main 2021 · 25 Feb · Shift 1 · Q55 with Solution

View written solutionFree

Correct answer: C

Understand the assertion

Thermal stress develops only when the expansion or contraction of a body is prevented or constrained.

For a rod lying freely, when heated, it is free to expand. Hence no internal restoring force is produced, so no thermal stress develops.

Therefore, Assertion A is true.
Understand the reason

On heating, the length of a rod generally increases due to thermal expansion: $\Delta L = \alpha L \Delta T$ where $\alpha$ is the coefficient of linear expansion.

Thus, Reason R is also true.
Check whether R explains A correctly

The assertion says that no thermal stress is developed in a freely lying rod.

The actual reason for this is:
- the rod is free to expand, so no opposing constraint exists,
- hence no stress is produced.
The statement "on heating, the length of the rod increases" is true, but this alone does not explain why stress is absent. Stress is absent because expansion is unrestrained, not merely because expansion occurs.
Evaluate options
- A: A is true but R is false — incorrect
- B: A is false but R is true — incorrect
- C: Both A and R are true but R is NOT the correct explanation of A — correct
- D: Both A and R are true and R is the correct explanation of A — incorrect

Therefore, the correct answer is C.

View written solutionFree

Correct answer: C

Understand the assertion

Thermal stress develops only when the expansion or contraction of a body is prevented or constrained.

For a rod lying freely, when heated, it is free to expand. Hence no internal restoring force is produced, so no thermal stress develops.

Therefore, Assertion A is true.
Understand the reason

On heating, the length of a rod generally increases due to thermal expansion: $\Delta L = \alpha L \Delta T$ where $\alpha$ is the coefficient of linear expansion.

Thus, Reason R is also true.
Check whether R explains A correctly

The assertion says that no thermal stress is developed in a freely lying rod.

The actual reason for this is:
- the rod is free to expand, so no opposing constraint exists,
- hence no stress is produced.
The statement "on heating, the length of the rod increases" is true, but this alone does not explain why stress is absent. Stress is absent because expansion is unrestrained, not merely because expansion occurs.
Evaluate options
- A: A is true but R is false — incorrect
- B: A is false but R is true — incorrect
- C: Both A and R are true but R is NOT the correct explanation of A — correct
- D: Both A and R are true and R is the correct explanation of A — incorrect

Therefore, the correct answer is C.