Temperature and Length Expansion – Rankers Physics

Thermal Expansion: Practice Problem & Solution

Assertion (A): Temperature of a rod is increased and again cooled to same initial temperature then its final length is equal to original length. Reason (R): For a small temperature change, length of a rod varies as \( l = l_0 (1+\alpha \Delta T) \) provided \( \alpha \Delta T is small  \). Here symbol have their usual meaning.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Thermal Expansion. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion is true as thermal expansion is reversible for elastic materials. Reason is the formula for linear expansion, \( l = l_0 (1+\alpha \Delta T) \), which confirms the assertion if \( \Delta T \) is reversed. Thus, both are true and (R) explains (A).

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