Thermal Expansion of Steel – Rankers Physics

Thermal Expansion: Practice Problem & Solution

Assertion (A): A temperature change which increases the length of a steel rod by ( 1% ) will increase its volume by ( 3% ). Reason (R): The coefficient of volume expansion is nearly three times the coefficient of linear expansion.  
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 (A) is true. If \( \frac{\Delta L}{L_0} = \alpha \Delta T = 0.01 \), then \( \frac{\Delta V}{V_0} = \gamma \Delta T \). Reason (R) is true, stating \( \gamma \approx 3\alpha \). Substituting, \( \frac{\Delta V}{V_0} \approx 3 (\alpha \Delta T) = 3(0.01) = 0.03 \), or ( 3% ). Thus, both are true and (R) correctly explains (A).

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